.999999999999...=1

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}.

That's right, but my point is that it's all the difference between .999... and 1.

Quote from: JoshuaZ on March 17, 2011, 01:53:17 PM

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 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...

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.

incorrect

entirely irrelevant to the matter at hand.

0.9999999 = 0.238%. QFT.

Any points that are not valid for real numbers are (shockingly) not valid for real numbers.

Quote from: Mr Pseudonym on March 17, 2011, 03:58:51 PM

0.9999999 = 0.238%. QFT.

QFT? Quoted for truth?

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.

Quote from: JoshuaZ on March 17, 2011, 04:10:59 PM

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.

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

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.

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. 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.

I'm using "cause" to mean "proves". This is fairly standard abuse of language.

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.

Quote from: JoshuaZ on March 17, 2011, 05:24:52 PM

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. 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.

Quote from: JoshuaZ on March 17, 2011, 05:24:52 PM

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.

Quote from: JoshuaZ on March 17, 2011, 05:24:52 PM

Well
I'm using "cause" to mean "proves". This is fairly standard abuse of language.

Abuse, not use.

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.

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.)

Quote

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.

Quote from: JoshuaZ on March 17, 2011, 06:47:04 PM

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 and all that. Anyways, I'm Joshua Zelinsky on that list.

Quote from: PizzaPlanet on March 17, 2011, 09:15:18 PM

Quote from: JoshuaZ on March 17, 2011, 06:47:04 PM

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 and all that. Anyways, I'm Joshua Zelinsky on that list.

Quote from: JoshuaZ on March 17, 2011, 10:32:18 PM

Quote from: PizzaPlanet on March 17, 2011, 09:15:18 PM

Quote from: JoshuaZ on March 17, 2011, 06:47:04 PM

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 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?

Quote from: Chris Spaghetti on March 17, 2011, 09:55:07 AM

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?

What's your native language? (Edit: German?)

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 .

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

Quote from: JoshuaZ on March 18, 2011, 06:58:37 AM

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 .

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 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.

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

.999999999999 ? 1

On the other hand, 0.9? = 1