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.999_=1, so does 1=2?


cmercein8
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let's make this simple. the OP states .999_ = 1


0.999... does not equal 1.0 no matter how you think about, put it, calculate it


it gets close but does not equal 1.0



Yes it does. There have already been about 4 or 5 proofs/demonstrations that show this.

It seems your flaw of thinking is that with 0.9999.... the 9s end at some point. Well they don't. They keep on going for infinity. If they did end at some point, then yes, you could say "it gets close but does not equal 1." But since they never end, it is equal to 1.

Look, no one ever said that it would be easy....

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Yes it does.
There have already been about 4 or 5 proofs/demonstrations that show this.


It seems your flaw of thinking is that with 0.9999.... the 9s end at some point. Well they don't. They keep on going for infinity. If they did end at some point, then yes, you could say "it gets close but does not equal 1." But since they never end, it is equal to 1.


Look, no one ever said that it would be easy....



No, it doesn't. It's as close as you can possibly get to 1 without actually getting 1. Also, whoever posted 9/9 = .999... is an idiot.

Morons.

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Yes it does. There have already been about 4 or 5 proofs/demonstrations that show this.


It seems your flaw of thinking is that with 0.9999.... the 9s end at some point. Well they don't. They keep on going for infinity. If they did end at some point, then yes, you could say "it gets close but does not equal 1." But since they never end, it is equal to 1.


Look, no one ever said that it would be easy....

 

But there is an infinite number of real numbers between 1.0 and 0.9999...

 

:o

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No, it doesn't. It's as
close
as you can possibly get to 1 without actually getting 1. Also, whoever posted 9/9 = .999... is an idiot.


Morons.

 

Nope; you're wrong. Look, I don't know what to say. Go up and read some of the 5 or so proofs that have already been shown. As long as the 9's go on for infinity, it is equal to one. End of story. There's no discussion to be had really; this is just math. If you don't understand it, it's likely just that you haven't learned about infinite sums or limits or whatnot. Or you've forgotten what you had learned.

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It was
Zeno.


I'd hand him an introductory calculus text and let him work it out for himself.



I argued this one with my Physics teacher...told him his statement of the problem was wrong....in the real world, the 'other side of the coliseum' is an arbitrary limit on the distance travelled...he was having none of it..and basically said the example illustrates the point he was trying to get across about calculus...he tried to pull the same {censored} about the tortoise never being able to catch the hare...pfft.

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Yes it does. There have already been about 4 or 5 proofs/demonstrations that show this.


It seems your flaw of thinking is that with 0.9999.... the 9s end at some point. Well they don't. They keep on going for infinity. If they did end at some point, then yes, you could say "it gets close but does not equal 1." But since they never end, it is equal to 1.


Look, no one ever said that it would be easy....



no. .999... approaches 1.0 but never reaches 1.0. there will always be an infinitesimal difference. always.

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I argued this one with my Physics teacher...told him his statement of the problem was wrong....in the real world, the 'other side of the coliseum' is an arbitrary limit on the distance travelled...he was having none of it..and basically said the example illustrates the point he was trying to get across about calculus...he tried to pull the same {censored} about the tortoise never being able to catch the hare...pfft.



I agree with you - what if the coliseum were only 1/2 as big?
Then the first assumption that you first have to cross the first half, would put you all the way across!!

I realize I'm arguing both sides of MY argument............

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Sigh. You clearly just don't know what you're talking about. The matter is resolved...



you are answering a different question of convergence. as terms are added to the series representing .999..., the function converges to 1.0, but that is not the same thing as stating .999... = 1.0

convergence is about finite limits. this is a mathematical requirement, else one could never solve a problem of distance as one object aproaches another because the distance is always halved, but obviously the distance between the two objects does approach Zero. convergence is a rule of necessity and of finite possibilities. that's not the case with .999... in this case, the number .999... will always have an infinitesimal difference with 1.0.

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are you thinking that the 9's literally repeat over time? there are always infinite 9s. remember .333... is equal to 1/3

.999... indicates an infinite number of terms in the series and yes the as the number of terms approaches infinity, .999... converges to 1.0, but this is not the same thing as stating .999... = 1.0

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That's the thing about the internet... it's brought together a lot of people with a complete contemptable lack of real education manifested in lots of blah blah woof woof about things they would like to think they know about but don't really.

 

I blame discovery channel and liberals!

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.999... indicates an infinite number of terms in the series and yes the as the number of terms approaches infinity, .999... converges to 1.0, but this is not the same thing as stating .999... = 1.0



This does not occur over time. There is no "approaching" here. If we were talking of a series such as .9, .99, .999, .99999999999999999999, .99999999999999999999999999999999999999999999, you would be correct, but .999... represents those 9s extending into infinity, in the present, right now, forever.

Thus equaling 1, by your own admission.

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This does not occur over time. There is no "approaching" here. If we were talking of a series such as .9, .99, .999, .99999999999999999999, .99999999999999999999999999999999999999999999, you would be correct, but .999... represents those 9s extending into infinity, in the present, right now, forever.


Thus equaling 1, by your own admission.

 

.999_ is less than 1 by an infinitely small difference, but a difference nonetheless.

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