The Flat Earth Society
Other Discussion Boards => Technology, Science & Alt Science => Topic started by: Tausami on March 15, 2011, 08:11:05 PM
-
(http://upload.wikimedia.org/math/4/7/e/47e0d646891053c1f3b41fa8c81b6ebb.png)
-
.999999999999=1
No.
-
.999999999999 ≠ 1
On the other hand, 0.9̅ = 1
-
*yawn*
-
ITT: 0.(9)=0.999999999999
Only not really.
-
ITT: TT (http://www.theflatearthsociety.org/forum/index.php?topic=21984.0)
-
(http://upload.wikimedia.org/math/4/7/e/47e0d646891053c1f3b41fa8c81b6ebb.png)
Fail.
-
(http://upload.wikimedia.org/math/4/7/e/47e0d646891053c1f3b41fa8c81b6ebb.png)
Fail.
Almost a quarter (0.238%) of all humanity would agree with you.
-
My calculator says you're right.
Mind you, in my job 0.5 = 1 (Also, 0.1=1 if we have to show integers on a spreadsheet) so I might not be the best man to speak to.
-
obvious statement is obvious.
-
http://en.wikipedia.org/wiki/0.999... (http://en.wikipedia.org/wiki/0.999...)
-
Almost a quarter (0.238%) of all humanity would agree with you.
Saw that coming, but still laff'd
-
This isn't really the best proof, either.
-
(http://upload.wikimedia.org/math/4/7/e/47e0d646891053c1f3b41fa8c81b6ebb.png)
1. Prove 1/9 = 0.111... then continue.
Having said that, I quite like this rather logical statement on the matter.
"If 0.999... does NOT equal 1, then please state the number in between."
-
"If 0.999... does NOT equal 1, then please state the number in between."
I imagine it would be 0.000...1.
-
(http://upload.wikimedia.org/math/4/7/e/47e0d646891053c1f3b41fa8c81b6ebb.png)
Fail.
Almost a quarter (0.238%) of all humanity would agree with you.
Please provide proof.
-
limx→∞(1 – 10-x) = 1 = 0.9̅
-
"If 0.999... does NOT equal 1, then please state the number in between."
I imagine it would be 1 - 0.000...1.
Fixed. Kinda.
-
"If 0.999... does NOT equal 1, then please state the number in between."
I imagine it would be 1 - 0.000...1.
Fixed. Kinda.
I would still disagree.
-
"If 0.999... does NOT equal 1, then please state the number in between."
I imagine it would be 1 - 0.000...1.
Fixed. Kinda.
I would still disagree.
I think the reason you might disagree is the same reason I put 'kinda'.
The pseudomath was off, but I fully acknowledge it as pseudomath.
-
I imagine it would be 0.000...1.
Which does not exist. You can't have an infinite amount of zeroes and something after that. That's not how infinity "works".
-
I imagine it would be 0.000...1.
Which does not exist. You can't have an infinite amount of zeroes and something after that. That's not how infinity "works".
Of course you can. ??? I've seen it many times, and I'm sure plenty of other people here have too.
-
"If 0.999... does NOT equal 1, then please state the number in between."
I imagine it would be 0.000...1.
Ok, you start writing that down for me and come back when you get to the 1.
-
This would roughly be equivalent to 0.000...1:
limx→∞(10-x)
So:
10-1 = 0.1
10-2 = 0.01
10-3 = 0.001
etc
So, if we solve for our limit, we get 0.
Thus, limx→∞(10-x) = 0. 0.000...1 is a nonsensical number. It is zero.
-
I guess the main problem is that one ninth is not 0.11111... it's just an approximation.
-
I guess the main problem is that one ninth is not 0.11111... it's just an approximation.
No. .1 would be an approximation. .11 would be an approximation. 0.11111... is equal to 1/9.
The statement made by the OP is orrect.
-
I guess the main problem is that one ninth is not 0.11111... it's just an approximation.
Prove to me that .1111...... is not 1/9.
In the field R (or any other such field), for a number not to be equal to another number, it must be less than or equal to that number.
if A=/=B, then either A>B or A<B. There's also a theorem regarding inequalities that gives us as a direct result, A>C>B or A<C<B.
so tell me, what number is between .11111111111................ and 1/9?
-
I imagine it would be 0.000...1.
Which does not exist. You can't have an infinite amount of zeroes and something after that. That's not how infinity "works".
Of course you can. ??? I've seen it many times, and I'm sure plenty of other people here have too.
I've seen it many times in maths arguments. Unfortunately, that doesn't make it any less incredibly wrong.
You see, infinity doesn't have an end. You can't put a one after the infinite amount of zeroes ends because, welp, it's infinite. The one never comes, the curtain never drops, the game is never concluded. In other words: 1-0.(9)=0.(0)=0
-
I imagine it would be 0.000...1.
Which does not exist. You can't have an infinite amount of zeroes and something after that. That's not how infinity "works".
Of course you can. ??? I've seen it many times, and I'm sure plenty of other people here have too.
I've seen it many times in maths arguments. Unfortunately, that doesn't make it any less incredibly wrong.
You see, infinity doesn't have an end. You can't put a one after the infinite amount of zeroes ends because, welp, it's infinite. The one never comes, the curtain never drops, the game is never concluded. In other words: 1-0.(9)=0.(0)=0
That's right, but my point is that it's all the difference between .999... and 1. If we accept that .000...1 is equal to 0, then .999... is equal to 1.
-
I've seen it many times in maths arguments. Unfortunately, that doesn't make it any less incredibly wrong.
You see, infinity doesn't have an end. You can't put a one after the infinite amount of zeroes ends because, welp, it's infinite. The one never comes, the curtain never drops, the game is never concluded. In other words: 1-0.(9)=0.(0)=0
Actually there are contexts where you can do this. There's nothing wrong with the ordering .000...1 as a map from the omega ordinal to {0,1}. The problem is that this isn't a meaningful real number.
That's right, but my point is that it's all the difference between .999... and 1. If we accept that .000...1 is equal to 0, then .999... is equal to 1.
No. .000...1 is not equal to 0.00...1 is just not a valid representation of a real number. Think about it this way: When I write something like .123 I mean 1/10 + 2/100 + 3/1000. Now, if I have a non-terminating expansion say 3.1415... then this means i have 3 + 1/10 + 4/100 + 1/1000 + 5/10000 which is a convergent series. Now, ask yourself, what series is represented by .000...1? There isn't any.
If you are still having trouble with this idea it might help to read an intro real analysis textbook which should make clear what is going on. The construction of reals from the rationals using either Dedekind cuts or Cauchy sequences will both make it clear what is going on.
-
Actually there are contexts where you can do this. There's nothing wrong with the ordering .000...1 as a map from the omega ordinal to {0,1}.
Which is both incorrect and entirely irrelevant to the matter at hand.
That's right, but my point is that it's all the difference between .999... and 1.
Yes, your point is that there is no difference. However, for some reason you also agree that there is a non-zero difference. This contradiction is what makes it funny.
-
Actually there are contexts where you can do this. There's nothing wrong with the ordering .000...1 as a map from the omega ordinal to {0,1}.
Which is both incorrect and entirely irrelevant to the matter at hand.
It isn't either of those. The point is that an ordering of the form given is self-consistent (http://en.wikipedia.org/wiki/Ordinal_number) so saying that "You can't put a one after the infinite amount of zeroes ends because, welp, it's infinite" is insufficient explanation. And in fact, there are number systems very close to the reals where you can do something very similar to this. The surreals would be one obvious example.
-
It isn't either of those. The point is that an ordering of the form given is self-consistent (http://en.wikipedia.org/wiki/Ordinal_number) so saying that "You can't put a one after the infinite amount of zeroes ends because, welp, it's infinite" is insufficient explanation. And in fact, there are number systems very close to the reals where you can do something very similar to this. The surreals would be one obvious example.
http://en.wikipedia.org/wiki/0.999... (http://en.wikipedia.org/wiki/0.999...)
denotes a real number that can be shown to be the number one. In other words, the symbols 0.999... and 1 represent the same number.
Any points that are not valid for real numbers are (shockingly) not valid for real numbers. In other words:
incorrect
Any points that are not valid for real numbers are also not relevant to real numbers, or:
entirely irrelevant to the matter at hand.
-
0.9999999 = 0.238%. QFT.
-
0.9999999 = 0.238%. QFT.
QFT? Quoted for truth?
-
Any points that are not valid for real numbers are (shockingly) not valid for real numbers.
Missing the point. You said "You can't put a one after the infinite amount of zeroes ends because, welp, it's infinite". That's not an explanation that's an argument by assertion. Since there are systems very similar to the reals where you can do that, the string being infinite is not at all sufficient explanation for why you can't do this.
-
0.9999999 = 0.238%. QFT.
QFT? Quoted for truth?
You know it PP.
-
Missing the point. You said "You can't put a one after the infinite amount of zeroes ends because, welp, it's infinite". That's not an explanation that's an argument by assertion.
It would seem you don't understand either the words "argument by assertion" or the word "infinite". Proof by assertion implies contradiction. Please point out the contradiction in "infinity is infinite".
Since there are systems very similar to the reals where you can do that, the string being infinite is not at all sufficient explanation for why you can't do this.
No, there are systems very similar to real numbers (also known as not real numbers) when you can do something very similar to that (also known as something else). The explanation is sufficient for real numbers, which is what this equity applies to, and which has already been stated. Invoking anything but real numbers here is a fallacy.
-
Since there are systems very similar to the reals where you can do that, the string being infinite is not at all sufficient explanation for why you can't do this.
No, there are systems very similar to real numbers (also known as not real numbers) when you can do something very similar to that (also known as something else). The explanation is sufficient for real numbers, which is what this equity applies to, and which has already been stated. Invoking anything but real numbers here is a fallacy.
No. Let's break this down. You said "You can't do X because of Y." where X is write 0.000...1 as a real number. I've then pointed out that "Well, but in system Z, you can X, but Y is till true." Given that, the problem isn't what is going on in Y. The problem is more subtle.
-
Yes, the problem was that we were talking about real numbers (and infinity) when you suddenly invoked other systems.
Let's go back to the basics:
Imagine a conversation where citizens of a certain American state are discussing whether or not it's good that they can't legally drink until they're 21. Then, I come in saying "HAHA I LIVE IN THE UK AND AM YOUNGER THAN 21 AND CAN DRINK. YOU ARE ALL WRONG NO MATTER WHAT YOU SAY". Did I make a convincing argument? Not for the laws of that state, no. Did I make a relevant comment? No.
Did you make a convincing argument? Not for real numbers, no.
Did you make a relevant argument? Not in the slightest.
On another note, what you didn't say before is "but Y is still true". If 0.(0)1 is a number (which it isn't), then 0.(9)=1-0.(0)1
-
To further elaborate on the claim that 0.(0)1 is a non-zero positive number.
a=0.(0)1
b=0.(0)1
a=b
a^2=ab
(a^2)-ab=0
(a^2)-ab+(b^2)=b^2
(a-b)^2=b^2
[0.(0)1-0.(0)1]=0.(0)1^2
0=0.(0)1^2
0=0.(0)1 (for two reasons. One of them being taking the square root, the other one being that we're considering 1*10^-infinity. That squared would be 1*10^-2infinity=1*10^-infinity)
-
Yes, the problem was that we were talking about real numbers (and infinity) when you suddenly invoked other systems.
Let's go back to the basics:
Imagine a conversation where citizens of a certain American state are discussing whether or not it's good that they can't legally drink until they're 21. Then, I come in saying "HAHA I LIVE IN THE UK AND AM YOUNGER THAN 21 AND CAN DRINK. YOU ARE ALL WRONG NO MATTER WHAT YOU SAY". Did I make a convincing argument? Not for the laws of that state, no. Did I make a relevant comment? No.
Did you make a convincing argument? Not for real numbers, no.
Did you make a relevant argument? Not in the slightest.
On another note, what you didn't say before is "but Y is still true". If 0.(0)1 is a number (which it isn't), then 0.(9)=1-0.(0)1
You've almost got it. Although Y here is the claim that the string is infinite. So let's focus on your analogy, and try to avoid the all caps. The proper analogy would be if the person in the UK then said "the key distinction is that in the US they passed laws in every state raising the drinking age to 21 because otherwise they states would lose federal highway funding" that would be a more thorough explanation. The problem is that saying essentially you can't do infinite things in the reals isn't helpful because sometimes you <i>and</i> there are systems very similar to the reals where you could do this. So it relies on other more suble properties of the reals.
An analogy that might help that is very similar to yours. Say it was in the early 1980s where most US states had a drinking age of 21 and a few had an age of 21. Then the statement about infinity becomes similar to someone saying that "You're not allowed to have alcohol because you are too young to drink" It answers the question in some very weak sense without giving any helpful context. In your situation it more severe, and this isn't a great analogy .
Suppose I have an axiomatic system S and T is a theorem of S. If a persona asks "why is T a theorem of S?" and you say "because of result A". Someone else coming along and saying "Well, but I have axiomatic system S' where A still hold and T doesn't" shows that whatever is causing T to hold in S is more than just A.
-
Again, "very similar" systems do not concern us. Please verify the meaning of the word "irrelevant".
You also confuse cause-effect relationships with proofs.
Edit: Also, I didn't say you can't do infinite things. I said that 1*10^-infinity is zero, and that 0.(0)1 is not a valid symbol.
See also: http://www.wolframalpha.com/input/?i=1%2A10%5E-infinity (http://www.wolframalpha.com/input/?i=1%2A10%5E-infinity)
For good measure, the same squared: http://www.wolframalpha.com/input/?i=1%2A10%5E%28-2infinity%29 (http://www.wolframalpha.com/input/?i=1%2A10%5E%28-2infinity%29)
-
Again, "very similar" systems do not concern us. Please verify the meaning of the word "irrelevant".
Ok. This is the point where I start being mildly obnoxious. I'm a grad student in math. (And because this sort of thing is difficult to verify on the internet, here is a list of the grad students in my department including my email. (http://www.bu.edu/math/people/graduate-students/) You are welcome to email me via that email address and confirm that that's me.
Now, speaking, as a mathematician, the above type of argument I gave with similar systems is standard. If I can present two systems that share some property, say being vorpal, and only one of the two systems has the the property that it goes snicker-snack, then being vorpal cannot be sufficient to force a system to go snicker-snack.
You also confuse cause-effect relationships with proofs.
I'm using "cause" to mean "proves". This is fairly standard abuse of language.
Edit: Also, I didn't say you can't do infinite things. I said that 1*10^-infinity is zero, and that 0.(0)1 is not a valid symbol.
Why don't we look at what I was responding to. You said ""You can't put a one after the infinite amount of zeroes ends because, welp, it's infinite" Note that this statement says nothing about whether 1*10^-infinity is zero and doesn't have the word "symbol" in it or any synonym thereof. If you are withdrawing this statement that's fine too.
-
Ok. This is the point where I start being mildly obnoxious. I'm a grad student in math. (And because this sort of thing is difficult to verify on the internet, here is a list of the grad students in my department including my email. (http://www.bu.edu/math/people/graduate-students/) You are welcome to email me via that email address and confirm that that's me.
I have no reasons not to believe you - you've already proven yourself sufficiently. However, the e-mail in your profile is hidden, so I can't really verify things.
Now, speaking, as a mathematician, the above type of argument I gave with similar systems is standard. If I can present two systems that share some property, say being vorpal, and only one of the two systems has the the property that it goes snicker-snack, then being vorpal cannot be sufficient to force a system to go snicker-snack.
Yes, but other systems no place in a conversation about one specific system. That's the whole point.
I'm using "cause" to mean "proves". This is fairly standard abuse of language.
Abuse, not use.
Why don't we look at what I was responding to. You said ""You can't put a one after the infinite amount of zeroes ends because, welp, it's infinite" Note that this statement says nothing about whether 1*10^-infinity is zero and doesn't have the word "symbol" in it or any synonym thereof. If you are withdrawing this statement that's fine too.
Yes, if it causes a misunderstanding, I'll happily re-word it so that there is no ambiguity to it. 0.(0)1 is not a valid symbol to describe any real number, and 1*10^-infinity, which is the difference between 1 and 0.(9), is equal to zero.
-
Ok. This is the point where I start being mildly obnoxious. I'm a grad student in math. (And because this sort of thing is difficult to verify on the internet, here is a list of the grad students in my department including my email. (http://www.bu.edu/math/people/graduate-students/) You are welcome to email me via that email address and confirm that that's me.
I have no reasons not to believe you - you've already proven yourself sufficiently. However, the e-mail in your profile is hidden, so I can't really verify things.
Er, I meant just emailing the email at the webpage and I could email back from that one. (The email in my profile here is actually different.)
Now, speaking, as a mathematician, the above type of argument I gave with similar systehttp://en.wikipedia.org/wiki/Ring_%28mathematics%29ms is standard. If I can present two systems that share some property, say being vorpal, and only one of the two systems has the the property that it goes snicker-snack, then being vorpal cannot be sufficient to force a system to go snicker-snack.
Yes, but other systems no place in a conversation about one specific system. That's the whole point.
Yes they do. Understanding a system comes in part from looking at how related systems behave. Let's take an example: that isn't our current one and is slightly more concrete: Let's say you want to understand why the integers have unique prime factorization. Well, maybe it follows from the integers being a ring (http://en.wikipedia.org/wiki/Ring_%28mathematics%29)? To show that that isn't the case, I can show you something that is almost like the integers- a ring that doesn't have unique prime factorization. Maybe, I give the example of numbers of the form a+b(-5)^(1/2) where a and b are integers. (In this ring it isn't that hard to see that 2*3=(1+(-5)^(1/2)) * (1+(-5)^(1/2)) violate unique prime factorization. So then you might say "well, that ring is really badly behaved. It doesn't have an order (that is there's no natural way given two elements deciding which is larger). And in fact, I could give an example of a ring which does have an order and still fails to have unique prime factorization. And we could keep playing this game, each time getting a better and better idea about what exactly it is about the integers that makes them have unique prime factorization.
Well
I'm using "cause" to mean "proves". This is fairly standard abuse of language.
Abuse, not use.
It doesn't make a difference here. If you prefer simple replace one with the other whenever you think it would make more sense.
0.(0)1 is not a valid symbol to describe any real number, and 1*10^-infinity, which is the difference between 1 and 0.(9), is equal to zero.
No disagreement there.
-
Er, I meant just emailing the email at the webpage and I could email back from that one. (The email in my profile here is actually different.)
Yes, which one from the long list of e-mails?
0.(0)1 is not a valid symbol to describe any real number, and 1*10^-infinity, which is the difference between 1 and 0.(9), is equal to zero.
No disagreement there.
Excellent.
-
Er, I meant just emailing the email at the webpage and I could email back from that one. (The email in my profile here is actually different.)
Yes, which one from the long list of e-mails?
Oh Sorry. I thought it was obvious from my user name which person was me. Illusion of transparency (http://lesswrong.com/lw/ke/illusion_of_transparency_why_no_one_understands/) and all that. Anyways, I'm Joshua Zelinsky on that list.
-
Er, I meant just emailing the email at the webpage and I could email back from that one. (The email in my profile here is actually different.)
Yes, which one from the long list of e-mails?
Oh Sorry. I thought it was obvious from my user name which person was me. Illusion of transparency (http://lesswrong.com/lw/ke/illusion_of_transparency_why_no_one_understands/) and all that. Anyways, I'm Joshua Zelinsky on that list.
I saw a Josh, not a Joshua. I'm not accustomed to the frivolity with which native English speakers deal with their names.
Also, by that logic you would have to assume that Tom Bishop's name is Tom Bishop (It isn't.), or that James is actually James (unlikely). And dare I even ask what my name would be?
-
Er, I meant just emailing the email at the webpage and I could email back from that one. (The email in my profile here is actually different.)
Yes, which one from the long list of e-mails?
Oh Sorry. I thought it was obvious from my user name which person was me. Illusion of transparency (http://lesswrong.com/lw/ke/illusion_of_transparency_why_no_one_understands/) and all that. Anyways, I'm Joshua Zelinsky on that list.
I saw a Josh, not a Joshua. I'm not accustomed to the frivolity with which native English speakers deal with their names.
Really? Interesting. It may be a function of what languages I'm familiar with but using a shortened or full form of a name is common in both of the two I'm most familiar with (although the other one where it is used one would probably not use a shortened name in a formal setting like a university directory. I'm not sure.) What's your native language? (Edit: German?)
Also, by that logic you would have to assume that Tom Bishop's name is Tom Bishop (It isn't.), or that James is actually James (unlikely). And dare I even ask what my name would be?
Well, the Tom example actually fits in with an interesting case. In Britain Tom is sometimes a full name but in the US it is invariably short for Thomas (and on very rare occasions Tomas). This leads to a certain puzzle in the Harry Potter books seem much more unfair to Americans .
-
I guess the main problem is that one ninth is not 0.11111... it's just an approximation.
Prove to me that .1111...... is not 1/9.
In the field R (or any other such field), for a number not to be equal to another number, it must be less than or equal to that number.
if A=/=B, then either A>B or A<B. There's also a theorem regarding inequalities that gives us as a direct result, A>C>B or A<C<B.
so tell me, what number is between .11111111111................ and 1/9?
Mathematically, we don't have a number which is exactly equal to 1/9. Before we had a concept of negative numbers it would have been impossible to demonstrate that 5-7=!0
0.111... is just a very good approximation which serves us for all purposes apart from in discussions arguing whether 0.999...=1
-
What's your native language? (Edit: German?)
Polish. We only get to use shortened forms and diminutives in very informal contexts.
Well, the Tom example actually fits in with an interesting case. In Britain Tom is sometimes a full name but in the US it is invariably short for Thomas (and on very rare occasions Tomas). This leads to a certain puzzle in the Harry Potter books seem much more unfair to Americans .
I think you misunderstood my. My point was that Tom Bishop's name is not Tom Bishop. Assuming that one's profile name is related to their real name is a bit of a stretch.
Mathematically, we don't have a number which is exactly equal to 1/9.
...
0.111... is just a very good approximation which serves us for all purposes apart from in discussions arguing whether 0.999...=1
No. We've just finished explaining why this is not the case! See the first post of this page.
-
What's your native language? (Edit: German?)
Polish. We only get to use shortened forms and diminutives in very informal contexts.
Ah. I should have known that too.
Well, the Tom example actually fits in with an interesting case. In Britain Tom is sometimes a full name but in the US it is invariably short for Thomas (and on very rare occasions Tomas). This leads to a certain puzzle in the Harry Potter books seem much more unfair to Americans .
I think you misunderstood my. My point was that Tom Bishop's name is not Tom Bishop. Assuming that one's profile name is related to their real name is a bit of a stretch.[/quote]
No I understood. I was then going off on a tangent about use of diminutive names. In general I'd think that if one sees a name very close where one has the shortened form and the last name data matches, and you were pointed to the page in question then one would conclude it was the same name. But it might be not obvious to a non-native speaker that Joshua and Josh are the same name.
Mathematically, we don't have a number which is exactly equal to 1/9.
...
0.111... is just a very good approximation which serves us for all purposes apart from in discussions arguing whether 0.999...=1
No. We've just finished explaining why this is not the case! See the first post of this page.
[/quote]
-
No I understood. I was then going off on a tangent about use of diminutive names. In general I'd think that if one sees a name very close where one has the shortened form and the last name data matches, and you were pointed to the page in question then one would conclude it was the same name. But it might be not obvious to a non-native speaker that Joshua and Josh are the same name.
I agree with you that it should be easy to spot. I guess I was subconsciously avoiding assumptions.
-
I'm gonna baaarrrf.
-
1/3 = 0.3'
2/3 = 0.6'
3/3 = 0.9'
??? ??? ???
-
::)
-
loldongs
-
Mathematically, we don't have a number which is exactly equal to 1/9.
>implying 1/9 isn't a number
Before we had a concept of negative numbers it would have been impossible to demonstrate that 5-7=!0
Incorrect.
0.111... is just a very good approximation which serves us for all purposes apart from in discussions arguing whether 0.999...=1
It's only an approximation if you don't indicate that the digits repeat infinitely. 0.11111 would be an approximation, 0.11111... is precise.
-
.999999999999 ? 1
On the other hand, 0.9? = 1
There is a major difference between, 9.999999999999999999999999999999999999999999999999999999 and 9.9.
If you want to simplify a repeating decimal, do it like this:
_
9.9
-
...I did. WTF are you talking about?
-
...I did. WTF are you talking about?
5th grade mathematics?
-
1/3 = 0.3'
2/3 = 0.6'
3/3 = 0.9'
??? ??? ???
This.
-
You don't even need to prove .9999 equals 1 because it's common sense and everybody knows it.
Nothing in this Universe approaches a number, gets all the way there, but never equals it.
-
You don't even need to prove .9999 equals 1 because it's common sense and everybody knows it.
Nothing in this Universe approaches a number, gets all the way there, but never equals it.
That doesn't even make sense.
-
It makes 100% sense to the non-morons of the world.
-
It makes 100% sense to the non-morons of the world.
Quiet. The adults are talking.
-
It makes 100% sense to the non-morons of the world.
Quiet. The adults are talking.
There are no adults here, just kids taking a break from Call of Duty or whacking off to porn.
-
It makes 100% sense to the non-morons of the world.
Quiet. The adults are talking.
There are no adults here, just kids taking a break from Call of Duty or whacking off to porn.
Actually, I'm doing both right now.
-
who cares about pointless idiot stupid stuff like this? seriously?? :'(
-
does anyone seriously take issue with the fact that .9 repeating = 1?
-
does anyone seriously take issue with the fact that .9 repeating = 1?
There are many nontrivial philosophical objections to the (typical, set theory based) concept of real numbers.
What I do not understand is why laypersons, not working in mathematics, care about such things.
It feels very sad to me that they are missing out on the beauty of serious mathematics.
-
IF you accept the real numbers, how can you possible reject it? I mean, 0.999... is a straight forward geometric series, S = ar/(1-r).
But something I'd be interested in is to see a proof that is compatible or uses portions from non-standard analysis and the hyperreal numbers. I believe there is a theorem that each hyperreal number is infinitely close to one and only one real number. Anyone familiar with this want to see what you can get into?
I think if 1 = 0.999..., then if 1 ≈ 1 + α and 0.999... ≈ 0.999... + β, then it would have to be true that α = β, wouldn't it? Could a proof be worked out that way? (≈ means "is infinitely close to" in this context, and α,β are infinitesimal)
EDIT- every thing I'm seeing indicates that in the hyperreal system 0.999... < 1 by an infinitesimal amount. ???
Before we had a concept of negative numbers it would have been impossible to demonstrate that 5-7=!0
Incorrect.
I'd like to see that.
-
Before we had a concept of negative numbers it would have been impossible to demonstrate that 5-7=!0
Incorrect.
I'd like to see that.
Add 7 to both sides of the equation.
-
It makes 100% sense to the non-morons of the world.
You reek of logical fallacies.
-
an infinitesimal amount.
In the set of real numbers, "an infinitesimal amount" = 0
-
an infinitesimal amount.
In the set of real numbers, "an infinitesimal amount" = 0
0 is not infinitesimal, it's easy to prove that the real number system contains no infinitesimals. It's a bit harder to construct number systems which do.
-
I am unaware of the existence of quotation marks.
k bro
-
I am unaware of the existence of quotation marks.
k bro
In case you didn't know, infinitesimal has a mathematical meaning..
Yes. Your point?
-
0 is not infinitesimal
False.
-
0 is not infinitesimal
False.
What a whopper of a first post. Unfortunately, you're wrong. Something that is infinitesimal cannot be equal to zero.
-
ITT: 0/∞ != 0
-
an infinitesimal amount.
In the set of real numbers, "an infinitesimal amount" = 0
If you read my post, I was not referring to the real numbers. I was referring to the hyperreal numbers. Anyone else care to take a stab at my question in my previous post? (seems non-standard analysis is none too popluar, sadly).
Here it is again:
IF you accept the real numbers, how can you possible reject it? I mean, 0.999... is a straight forward geometric series, S = ar/(1-r).
But something I'd be interested in is to see a proof that is compatible or uses portions from non-standard analysis and the hyperreal numbers. I believe there is a theorem that each hyperreal number is infinitely close to one and only one real number. Anyone familiar with this want to see what you can get into?
I think if 1 = 0.999..., then if 1 ≈ 1 + α and 0.999... ≈ 0.999... + β, then it would have to be true that α = β, wouldn't it? Could a proof be worked out that way? (≈ means "is infinitely close to" in this context, and α,β are infinitesimal)
EDIT- every thing I'm seeing indicates that in the hyperreal system 0.999... < 1 by an infinitesimal amount. ???
It seems 0.999... is not equal to 1 in the hyperreals. I'm wondering if that is false, and if so I want to see a proof that 0.999... = 1 in the hyperreal system.
0 is not infinitesimal
False.
What a whopper of a first post. Unfortunately, you're wrong. Something that is infinitesimal cannot be equal to zero.
In non-standard analysis (infinitesimal calculus as described by Abraham Robinson), 0 is an infinitesimal number, if I recall correctly. Because st(x + Δx) = x, and st(x + 0) = x. Of course, I haven't looked in his free textbook for a few months, so I could be misremembering.
-
0,9999999999999...... <> 1
0,9999999999999...... it is NOT 1
There are infinite real numbers between 0 and 1, this lead us to the fact that for any iota ( ANY ) that allows me to consider:
x+i = 1, even if x= 0,99999999999999999.. ( you put as many 9's here as you want ), "i" is still NOT 0
You can say that 0,9999999.... is 1 in the limit ( Lim x-> 1 ; y=x ) Please, forgive this poor mathematic notation, just get the idea.
-
0,9999999999999...... <> 1
0,9999999999999...... it is NOT 1
There are infinite real numbers between 0 and 1, this lead us to the fact that for any iota ( ANY ) that allows me to consider:
x+i = 1, even if x= 0,99999999999999999.. ( you put as many 9's here as you want ), "i" is still NOT 0
You can say that 0,9999999.... is 1 in the limit ( Lim x-> 1 ; y=x ) Please, forgive this poor mathematic notation, just get the idea.
If you are talking about real numbers, 0.999... IS equal to 1.
-
0,9999999999999...... <> 1
0,9999999999999...... it is NOT 1
There are infinite real numbers between 0 and 1, this lead us to the fact that for any iota ( ANY ) that allows me to consider:
x+i = 1, even if x= 0,99999999999999999.. ( you put as many 9's here as you want ), "i" is still NOT 0
You can say that 0,9999999.... is 1 in the limit ( Lim x-> 1 ; y=x ) Please, forgive this poor mathematic notation, just get the idea.
0.(9) has infinite 9s.
-
There are infinite real numbers between 0 and 1, this lead us to the fact that for any iota ( ANY ) that allows me to consider:
x+i = 1, even if x= 0,99999999999999999.. ( you put as many 9's here as you want ), "i" is still NOT 0
The fact that there are infinite 9s cancels out the fact that there are infinite numbers between 0 and 1. Would you dispute the fact that 0,333... is equal to 1/3? If you do, I wish you luck in the third grade; if not, I hope you realize that it is the same principle at work here. Technically you can put as many 3s after the decimal point you want, it will still not be equal to 1/3 (which by definition can't be expressed by a terminating decimal anyway); but if it's understood that there are an infinite number of 3s after the decimal point, it is equal to 1/3.
0,333... x 3 = 0,999...; do you dispute the logic?
1/3 x 3 = 1; do you dispute the math?
Therefore, 0,999... = 1.
In other words, there is no iota.
-
Is using commas as decimal points a convention that I am not aware of?
-
Is using commas as decimal points a convention that I am not aware of?
In many places (including all of Europe, I believe) it is the convention. I'm American, of course, I just thought I'd humour him.
-
It's not all of Europe, but several countries do do it. That's the way I've been taught, and I had to go through a painful switching process when I moved to the UK.
Basically, those countries use a comma as a decimal point and a dot as a separator in large numbers.
0,5 would be 1/2, whereas 1.000.000 would be one million.
The reason for that is that (mostly in handwriting), it's fairly easy to not write down the dot (for example, by simply not pressing your pen hard enough), which is generally much less likely with a comma. If we miss a separator, on the other hand, it's usually no big deal (I mean, hardly anyone even uses them).
-
First of all yes, please forgive my European notation ;-)
There are infinite real numbers between 0 and 1, this lead us to the fact that for any iota ( ANY ) that allows me to consider:
x+i = 1, even if x= 0,99999999999999999.. ( you put as many 9's here as you want ), "i" is still NOT 0
The fact that there are infinite 9s cancels out the fact that there are infinite numbers between 0 and 1. Would you dispute the fact that 0,333... is equal to 1/3? If you do, I wish you luck in the third grade; if not, I hope you realize that it is the same principle at work here. Technically you can put as many 3s after the decimal point you want, it will still not be equal to 1/3 (which by definition can't be expressed by a terminating decimal anyway); but if it's understood that there are an infinite number of 3s after the decimal point, it is equal to 1/3.
0,333... x 3 = 0,999...; do you dispute the logic?
1/3 x 3 = 1; do you dispute the math?
Therefore, 0,999... = 1.
In other words, there is no iota.
About the topic; I am not discussing the logic nor the math. However..... (1/3) X 3 = 1 ... Absolutely OK, nothing to say..
0,3333 X 3 = 0,9999 .... how many 3?
Maybe this is just spinning out; what I say is that THERE is, a difference, a Iota, between these infinite "3", or "9", and the complete number. It is just out of convenience, and because it is much better, that we type 1/3 instead of the zillions of 3`s ... and this is precisely the point... 1/3 is a solid complete number; so it is 1.
I understand your point ( for real), but I only can accept that 0,999999 (period) IS 1 as APROXIMATION.
Again, for most common uses, even Pi can be considered as 3,1416 ... but it is NOT. Pi is Pi ..... and NO short description of Pi ( even with zillions of numbers) is Pi
1) (1/3) + (1/3) + (1/3) = 1
2 ) The 0,3333 version.......... I cannot support it from an strict mathematical point of view. Again, I can accept it as approximation.
I'd use a pregnancy simile.. but unsure if it's out of rules :-P
-
First of all yes, please forgive my European notation ;-)
There are infinite real numbers between 0 and 1, this lead us to the fact that for any iota ( ANY ) that allows me to consider:
x+i = 1, even if x= 0,99999999999999999.. ( you put as many 9's here as you want ), "i" is still NOT 0
The fact that there are infinite 9s cancels out the fact that there are infinite numbers between 0 and 1. Would you dispute the fact that 0,333... is equal to 1/3? If you do, I wish you luck in the third grade; if not, I hope you realize that it is the same principle at work here. Technically you can put as many 3s after the decimal point you want, it will still not be equal to 1/3 (which by definition can't be expressed by a terminating decimal anyway); but if it's understood that there are an infinite number of 3s after the decimal point, it is equal to 1/3.
0,333... x 3 = 0,999...; do you dispute the logic?
1/3 x 3 = 1; do you dispute the math?
Therefore, 0,999... = 1.
In other words, there is no iota.
About the topic; I am not discussing the logic nor the math. However..... (1/3) X 3 = 1 ... Absolutely OK, nothing to say..
0,3333 X 3 = 0,9999 .... how many 3?
Maybe this is just spinning out; what I say is that THERE is, a difference, a Iota, between these infinite "3", or "9", and the complete number. It is just out of convenience, and because it is much better, that we type 1/3 instead of the zillions of 3`s ... and this is precisely the point... 1/3 is a solid complete number; so it is 1.
I understand your point ( for real), but I only can accept that 0,999999 (period) IS 1 as APROXIMATION.
Again, for most common uses, even Pi can be considered as 3,1416 ... but it is NOT. Pi is Pi ..... and NO short description of Pi ( even with zillions of numbers) is Pi
1) (1/3) + (1/3) + (1/3) = 1
2 ) The 0,3333 version.......... I cannot support it from an strict mathematical point of view. Again, I can accept it as approximation.
I'd use a pregnancy simile.. but unsure if it's out of rules :-P
Good luck in the third grade.
-
You obviously don't grasp the concept of infinity.
-
About the topic; I am not discussing the logic nor the math. However..... (1/3) X 3 = 1 ... Absolutely OK, nothing to say..
0,3333 X 3 = 0,9999 .... how many 3?
Maybe this is just spinning out; what I say is that THERE is, a difference, a Iota, between these infinite "3", or "9", and the complete number. It is just out of convenience, and because it is much better, that we type 1/3 instead of the zillions of 3`s ... and this is precisely the point... 1/3 is a solid complete number; so it is 1.
So what is this number that comes after infinity?
-
Infinity and a half, duh.
-
I thought it was infinity + 1 :-D
I will revise my 4th grade concepts :-D
Anyway, since I am going to have vacation tomorrow I will take calculus again ;-)
-
OK, anyone can rectify and some1 said it is wise to do so.
After some mathematical research ( beyond 3rd grade ;-) I must change my opinion and recognize that after all 0.999999999999..... is as well a valid representation of 1
Please, accept my apologies for all previous messages since I understand that I should have made this research before posting.
have a good day.
-
OK, anyone can rectify and some1 said it is wise to do so.
After some mathematical research ( beyond 3rd grade ;-) I must change my opinion and recognize that after all 0.999999999999..... is as well a valid representation of 1
Please, accept my apologies for all previous messages since I understand that I should have made this research before posting.
have a good day.
You mean, you looked this up on google?
-
OK, anyone can rectify and some1 said it is wise to do so.
After some mathematical research ( beyond 3rd grade ;-) I must change my opinion and recognize that after all 0.999999999999..... is as well a valid representation of 1
Please, accept my apologies for all previous messages since I understand that I should have made this research before posting.
have a good day.
You mean, you looked this up on google?
Can the internet not be used for valid research?
-
OK, anyone can rectify and some1 said it is wise to do so.
After some mathematical research ( beyond 3rd grade ;-) I must change my opinion and recognize that after all 0.999999999999..... is as well a valid representation of 1
Please, accept my apologies for all previous messages since I understand that I should have made this research before posting.
have a good day.
You mean, you looked this up on google?
No, I mean that I consulted some mathematician friends, and that I revised some Math books, and therefore I changed my mind
:-)
-
OK, anyone can rectify and some1 said it is wise to do so.
After some mathematical research ( beyond 3rd grade ;-) I must change my opinion and recognize that after all 0.999999999999..... is as well a valid representation of 1
Please, accept my apologies for all previous messages since I understand that I should have made this research before posting.
have a good day.
You mean, you looked this up on google?
Can the internet not be used for valid research?
Of course it can. However, mathematical research sounds like he is trying a lot harder than just putting 0.999 into a google search and going to the first answer on the search page result. That so happens to be the Wiki page that says this about the situation;
"In mathematics, the repeating decimal 0.999... (which may also be written as 0.9, , 0.(9), or as 0. followed by any number of 9s in the repeating decimal) denotes a real number that can be shown to be the number one. In other words, the symbols 0.999... and 1 represent the same number"
That took me all of about 5 seconds to find. It explains it all and even includes this little number (pardon the pun);
With the rise of the Internet, debates about 0.999... have escaped the classroom and are commonplace on newsgroups and message boards, including many that nominally have little to do with mathematics.
-
Also from the same wiki page;
Q: How many mathematicians does it take to screw in a lightbulb?
A: 0.999999....
-
It's not all of Europe, but several countries do do it. That's the way I've been taught, and I had to go through a painful switching process when I moved to the UK.
Basically, those countries use a comma as a decimal point and a dot as a separator in large numbers.
0,5 would be 1/2, whereas 1.000.000 would be one million.
Sorry to back to sort of off topic, but are saying that in the we write 1 million as 1.000.000 and 1/2 as 0,5 ?
We don't. Then again I may have misread your post and you infact meant that other coutries do the above but that the UK do not.