0.9... = 1

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Erasmus

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0.9... = 1
« Reply #30 on: November 07, 2006, 12:05:55 PM »
Quote from: "BOGWarrior89"
Ok, now try multiplying 0.9999... by a number that isn't base ten (like 2, for instance).


Sure, well, the first step would be to convert one or both into a different form so that they are both in the same form.  For example, converting the base-2 number to base-10 is a good start, or just writing 0.999... as 1 (even easier).  

What is this supposed to accomplish?
Why did the chicken cross the Möbius strip?

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Erasmus

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0.9... = 1
« Reply #31 on: November 07, 2006, 12:09:16 PM »
Quote from: "BOGWarrior89"
Wrong; 1/9 = 0.1111... + 1/(9 * infinity).


"infinity" isn't a number.  Please stop using it as if it were.

Let's get to a meta-discussion here: do you know that you're talking nonsense, how the mathematics of these "disputed" concepts (infinite repeating decimals; transfinite cardinals) and are just trying to use it to make a point?  If so, maybe you could just state your point now, because it's not clear to me.  If not, please don't try to state any point because I'm certain that while it may not be wrong, it will certainly not follow from the arguments you've put here.
Why did the chicken cross the Möbius strip?

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BOGWarrior89

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0.9... = 1
« Reply #32 on: November 07, 2006, 12:37:23 PM »
Quote from: "Erasmus"
Quote from: "BOGWarrior89"
Wrong; 1/9 = 0.1111... + 1/(9 * infinity).


"infinity" isn't a number.  Please stop using it as if it were.

Let's get to a meta-discussion here: do you know that you're talking nonsense, how the mathematics of these "disputed" concepts (infinite repeating decimals; transfinite cardinals) and are just trying to use it to make a point?  If so, maybe you could just state your point now, because it's not clear to me.  If not, please don't try to state any point because I'm certain that while it may not be wrong, it will certainly not follow from the arguments you've put here.


"infinity" is a number.  It can be defined as "the largest possible number in a set."  Therefore, it exists.  The reciprocal of infinity (1/infinity) can be defined as "the smallest positive number."  Therefore, it exists.  Only human logic prevents you from formally giving "infinity" and its reciprocal a value.

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Erasmus

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« Reply #33 on: November 07, 2006, 12:43:10 PM »
Quote from: "BOGWarrior89"
"infinity" is a number.  It can be defined as "the largest possible number in a set."


No, it can't.  First I would ask you which set it's the largest number in; next, I would remind you that not all sets have largest elements: consider the set of positive numbers: if you pick any element from the set and claim it to be the biggest, I can find a bigger one by, for example, adding 1 to that number.  Therefore the set of positive numbers doesn't have a largest element, since the largest element cannot be smaller than any other element.
Why did the chicken cross the Möbius strip?

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BOGWarrior89

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« Reply #34 on: November 07, 2006, 12:46:50 PM »
Quote from: "Erasmus"
Quote from: "I"
"infinity" is a number.  It can be defined as "the largest possible number in a set."


No, it can't.  First I would ask you which set it's the largest number in; next, I would remind you that not all sets have largest elements: consider the set of positive numbers: if you pick any element from the set and claim it to be the biggest, I can find a bigger one by, for example, adding 1 to that number.  Therefore the set of positive numbers doesn't have a largest element, since the largest element cannot be smaller than any other element.

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Quote from: "I"
Only human logic prevents you from formally giving "infinity" and its reciprocal a value.

LET IT GO FOR TWO SECONDS.  You'll see what I mean.

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Erasmus

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« Reply #35 on: November 07, 2006, 12:53:34 PM »
Quote from: "BOGWarrior89"
LET IT GO FOR TWO SECONDS.  You'll see what I mean.


What are you talking about?
Why did the chicken cross the Möbius strip?

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BOGWarrior89

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« Reply #36 on: November 07, 2006, 01:00:44 PM »
Quote from: "Erasmus"
Quote from: "BOGWarrior89"
LET IT GO FOR TWO SECONDS.  You'll see what I mean.


What are you talking about?


It's hard to explain, due to my lack of ability, so I'll try my best: just because you can't come up with a reason for something, doesn't automatically disqualify it from being the "truth".  It just means someone else will do it for you.  All ideas have equal footing to be the "truth"; only our brains, pride, prejudice, arrogance, and "intelligence" states that some views are more favorable over other views.  Anything can be the "truth", but, relative to our thought processes, definitions, beliefs, and ideas, some are rejected as "nonsense" and others are adopted.  This is the reason why we fight, because, relative to our beliefs, what we are fighting for is the best way to do something.  It all comes back to psychology.

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Erasmus

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« Reply #37 on: November 07, 2006, 01:18:37 PM »
Quote from: "BOGWarrior89"
just because you can't come up with a reason for something, doesn't automatically disqualify it from being the "truth".


That's very interesting but, in this particular case, we came up with a reasons for certain statements to be true, whereas you merely said that our statements were false, and gave no reasons.  So this admonition doesn't really apply, does it?

Quote
All ideas have equal footing to be the "truth"; only our brains, pride, prejudice, arrogance, and "intelligence" states that some views are more favorable over other views.


What you basically seem to be saying is that nobody can ever say that anything is true or false, in any domain.  If that's the case, what's the point of discussing the issues at all?  The fact is that the human assumption that some views are better than others has proven useful, has enabled us to "build bridges" as I like to say.  You can spout your "nothing is really true or false" propaganda all you like, but in the end, people want bridges, so nobody's going to care about your idea unless they are equally disinterested in being productive members of the intellectual community.

While you're pondering that, you may want to register in a math course of some kind for next semester.  It will help make you a physicist.
Why did the chicken cross the Möbius strip?

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BOGWarrior89

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« Reply #38 on: November 07, 2006, 01:23:05 PM »
I'm saying there is no way to check our answers.  Life is all about uncertainty.

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Erasmus

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« Reply #39 on: November 07, 2006, 01:25:15 PM »
Quote from: "BOGWarrior89"
I'm saying there is no way to check our answers.  Life is all about uncertainty.


Actually, you're not saying anything, so I think this conversation is done.
Why did the chicken cross the Möbius strip?

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BOGWarrior89

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0.9... = 1
« Reply #40 on: November 07, 2006, 01:25:47 PM »
Quote from: "Erasmus"
Quote from: "BOGWarrior89"
just because you can't come up with a reason for something, doesn't automatically disqualify it from being the "truth".


That's very interesting but, in this particular case, we came up with a reasons for certain statements to be true, whereas you merely said that our statements were false, and gave no reasons.  So this admonition doesn't really apply, does it?


I'm trying to get you to understand why you got the answer "0.99999... = 1".

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beast

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0.9... = 1
« Reply #41 on: November 07, 2006, 01:30:07 PM »
Quote from: "BOGWarrior89"


It's hard to explain, due to my lack of ability, so I'll try my best: just because you can't come up with a reason for something, doesn't automatically disqualify it from being the "truth".  It just means someone else will do it for you.  All ideas have equal footing to be the "truth"; only our brains, pride, prejudice, arrogance, and "intelligence" states that some views are more favorable over other views.  Anything can be the "truth", but, relative to our thought processes, definitions, beliefs, and ideas, some are rejected as "nonsense" and others are adopted.  This is the reason why we fight, because, relative to our beliefs, what we are fighting for is the best way to do something.  It all comes back to psychology.


Translation: you don't know what you're talking about and you're a n00b.  While what you say may be true, it's really completely irrelevant to the mathematical proofs put forward in this topic.  Truth may be relative to our own perspective but it is a safe assumption that when somebody writes a mathematical proof they are putting it in the context of mathematics.  Thus if you want to say that it's wrong, you need to demonstrate it's falsehood mathematically.

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BOGWarrior89

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« Reply #42 on: November 07, 2006, 01:34:17 PM »
Quote from: "beast"
Quote from: "BOGWarrior89"


It's hard to explain, due to my lack of ability, so I'll try my best: just because you can't come up with a reason for something, doesn't automatically disqualify it from being the "truth".  It just means someone else will do it for you.  All ideas have equal footing to be the "truth"; only our brains, pride, prejudice, arrogance, and "intelligence" states that some views are more favorable over other views.  Anything can be the "truth", but, relative to our thought processes, definitions, beliefs, and ideas, some are rejected as "nonsense" and others are adopted.  This is the reason why we fight, because, relative to our beliefs, what we are fighting for is the best way to do something.  It all comes back to psychology.


Translation: you don't know what you're talking about and you're a n00b.  While what you say may be true, it's really completely irrelevant to the mathematical proofs put forward in this topic.  Truth may be relative to our own perspective but it is a safe assumption that when somebody writes a mathematical proof they are putting it in the context of mathematics.  Thus if you want to say that it's wrong, you need to demonstrate it's falsehood mathematically.

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Quote from: "BOGWarrior89"
Fucktards, that just shows that something is lost in translation from fractions to decimals.


I think I already did.

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beast

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0.9... = 1
« Reply #43 on: November 07, 2006, 01:37:42 PM »
That's not a mathematical proof.  We've seen a couple of different variations of mathematical proofs and they demonstrated the same result.

Also what is lost in the translation between fractions and decimals?

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BOGWarrior89

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0.9... = 1
« Reply #44 on: November 07, 2006, 01:40:59 PM »
Quote from: "beast"
That's not a mathematical proof.  We've seen a couple of different variations of mathematical proofs and they demonstrated the same result.

Also what is lost in the translation between fractions and decimals?


1/3 = 0.33333...

One cannot be divided by three to it's fullest, because 10/3 = 9 Remainder 1, which is then transformed into 10, which is then divided by three again.  The process is endless, so you never fully divide one by three.

So, therefore, there must be some kind of correctional constant - hence my use of the 1/(3 * infinity).

1/3 = 0.3333333... +1/(3*infinity)

Multiply both sides by three ...

(1/3)(3) = 0.99999... + (3)(1/(3*infinity))
1 = 0.999999... + 1/infinity

Therefore, 1/infinity is the smallest possible positive number: 0.00000...1

0.9... = 1
« Reply #45 on: November 07, 2006, 02:03:24 PM »
Quote from: "BOGWarrior89"
I'm saying there is no way to check our answers. Life is all about uncertainty.


You need to study epistemology.  We can check our answers within a given methodology.
ooyakasha!

0.9... = 1
« Reply #46 on: November 07, 2006, 02:04:49 PM »
Quote
Therefore, 1/infinity is the smallest possible positive number: 0.00000...1


You have to add zeros infinitely.  The limit is just zero.
 captain is sailing through the arctic. The first mate runs up and says to him, "captain, there is an iceberg dead ahead. What should we do?" The captain looks at the iceberg, then glances at his map and says, "there's no iceberg here! Keep going!"

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beast

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« Reply #47 on: November 07, 2006, 02:13:35 PM »
Infinity is not a number.

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Ubuntu

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« Reply #48 on: November 07, 2006, 02:16:21 PM »
Quote from: "fathomak"
I think this is a better question:

Which is larger, the set of all positive real integers, or the set of all primes?


How can infinity be greater than infinity? It's not even a number, really...

0.9... = 1
« Reply #49 on: November 07, 2006, 02:19:47 PM »
Quote from: "BOGWarrior89"
I'm saying there is no way to check our answers.  Life is all about uncertainty.


It is true you cannot prove causality.  But you can get what seems to be ridiculously close.

In statistics there is a law called "The Law of Large Numbers".  Despite how interesting and action-packed this mathematical theorem is, it relates to the relationship of sample size to the outcome.  The larger the sample, the closer the outcome reflects the truth.  Of course, this is just statistics.

Hume's famous anecdote reguarding this was the room.  Could you prove conclusively that the next time you come to the room it will still be there?  What about if you came and left 999 times, would it be there the 1,000th?

But there is some point where we accept 99% certainty.  Otherwise our abstract world would be too chaotic to function in.
ttp://theflatearthsociety.org/forums/search.php

"Against criticism a man can neither protest nor defend himself; he must act in spite of it, and then it will gradually yield to him." -Johann Wolfgang von Goethe

0.9... = 1
« Reply #50 on: November 07, 2006, 02:31:29 PM »
Quote from: "Ubuntu"
Quote from: "fathomak"
I think this is a better question:

Which is larger, the set of all positive real integers, or the set of all primes?


How can infinity be greater than infinity? It's not even a number, really...


One infinity can be greater than another, comparitive in the rate that the two infinities rise.

for example, lim as x->infinity (x) is simply infinity, but lim as x-infinity (2x^2) reaches infinity faster, so it is said to be greater.
he man in black fled across the desert, and the gunslinger followed.

Advocatus Diaboli

0.9... = 1
« Reply #51 on: November 07, 2006, 02:36:29 PM »
Infinity is a verbal concept, not an actual number.

Simply put, the term infinity refers to a limitless, never ending, and increasing amount.

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Ubuntu

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« Reply #52 on: November 07, 2006, 02:38:44 PM »
Quote from: "BOGWarrior89"
The process is endless, so you never fully divide one by three.


Problem here: numbers aren't processes.

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Ubuntu

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0.9... = 1
« Reply #53 on: November 07, 2006, 02:40:37 PM »
Quote from: "CrimsonKing"
Quote from: "Ubuntu"
Quote from: "fathomak"
I think this is a better question:

Which is larger, the set of all positive real integers, or the set of all primes?


How can infinity be greater than infinity? It's not even a number, really...


One infinity can be greater than another, comparitive in the rate that the two infinities rise.

for example, lim as x->infinity (x) is simply infinity, but lim as x-infinity (2x^2) reaches infinity faster, so it is said to be greater.


"Reaches"?

0.9... = 1
« Reply #54 on: November 07, 2006, 02:40:44 PM »
Quote from: "jaybird39"
Simply put, the term infinity refers to a limitless, never ending, and increasing amount.


yea, so, if this amount increases faster, than it is greater at any given point, meaning that it is greater.
he man in black fled across the desert, and the gunslinger followed.

Advocatus Diaboli

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Ubuntu

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0.9... = 1
« Reply #55 on: November 07, 2006, 02:42:42 PM »
Quote from: "CrimsonKing"
Quote from: "jaybird39"
Simply put, the term infinity refers to a limitless, never ending, and increasing amount.


yea, so, if this amount increases faster, than it is greater at any given point, meaning that it is greater.


What if infinity doesn't increase? That is to say, it has infinite numeric value, not an infinitely increasing numeric value.

0.9... = 1
« Reply #56 on: November 07, 2006, 02:44:56 PM »
theres no such thing as a numerical infinity, it makes no sense, it has to be a conceptual thing, always increasing... because even arbitrarily large numbers can have one added to them.
he man in black fled across the desert, and the gunslinger followed.

Advocatus Diaboli

0.9... = 1
« Reply #57 on: November 07, 2006, 02:45:55 PM »
Well, here's the answer (I think) to my previous question:

Quote from: "fathomak"
Which is larger, the set of all positive real integers or the set of all primes?


First we have to show that the set of all primes is, in fact, infinite.  Fortunately, Euclid has done this for us:
http://primes.utm.edu/notes/proofs/infinite/euclids.html



So now I am going to claim they are equal.  To do so, lets define a few conditions:

Let P be the set of all primes {p1, p2, ...pm}, where pi = pj if and only if i = j.

Let S be the set of all positive real integers {1, 2, ...n}.

Now we will define R to be a transformation from S to P (R: S -> P) such that for some element s in S, R(s) = ps

It is easy to see that the mapping R: S -> P is one-to-one.

Consider a and b, elements of the set S.  Then if R(a) = R(b), it implies a = b.
R(a) = pa
R(b) = pb

Then pa = pb, but pi = pj if and only if i = j, so we conclude that a = b, and R: S -> P is one-to-one.

It is also easy to see that R: S -> P is onto, for any pk in P can be obtained by R(k).

Since R is one-to-one and onto, we can conclude that the sets are the same size.



QED
 captain is sailing through the arctic. The first mate runs up and says to him, "captain, there is an iceberg dead ahead. What should we do?" The captain looks at the iceberg, then glances at his map and says, "there's no iceberg here! Keep going!"

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cadmium_blimp

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0.9... = 1
« Reply #58 on: November 07, 2006, 02:59:38 PM »
I'd like to interject here with something I've been thinking about for awhile.  Could it be possible that zero is infinite since it is infinitely smaller than the smallest number?  Zero is complete absence of whatever and a complete absence of something is a whole lot of nothing, if you catch my drift.

Quote from: Commander Taggart
Never give up, never surrender!

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Ubuntu

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« Reply #59 on: November 07, 2006, 03:00:32 PM »
Quote from: "fathomak"
QED


When are you actually going to get around to doing that?