Proof that 0.999... = 1

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Why ?

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I have to agree, that is pretty sweet.

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Rather unusual that someone decides that they should start a thread on this rather than its negation. And somewhat pleasing.

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I think the "in popular culture" section is particularly hilarious.

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This is awesome
As awesome as a picture of the Riemann Zeta Function over the Critical Strip?

I think not.

But seriously now, with something so fundamentally obvious, there will always be a lot of proofs for it and you can make the proofs as absurdly complicated as you like. Because of this I kind of see proving things that aren't very exciting to be a bit a waste of time and intellect. (actually, proving things in general isn't all that fun but that's not the point).

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As awesome as a picture of the Riemann Zeta Function over the Critical Strip?

I think not.

As if that's anywhere nearly as cool as the Rule 30 CA:

But seriously now' date=' with something so fundamentally obvious, there will [i']always[/i] be a lot of proofs for it and you can make the proofs as absurdly complicated as you like. Because of this I kind of see proving things that aren't very exciting to be a bit a waste of time and intellect. (actually, proving things in general isn't all that fun but that's not the point).

They would be, if people weren't so goddamn insistant that the proofs are nonexistent/wrong/logically flawed in some way.

The same holds true for finding statistical distributions of the plaintext in OTP with random ciphertext. I've had people try to argue with me that the ciphertext isn't at least as statistically random as the pad, and that with enough statistical modelling you can recover the plaintext.

It's nice that people are starting to stick proofs like this in Wikipedia, so that if someone tries to assert something which has proven to be the opposite, you can just hand them the link, rather than having to argue.

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• 1 month later...

I seem to remember a long time ago me and matt grime were having an argument on this same subject, but more specifically on its relation to the physical world. I said how would it be possible to have in physical existance a quantity that had a non-terminating decimal expansion. I thought it would be impossible, because how could some quantity, which exists, be a value which never terminates, if u get wat i mean? like, the decimals go on forever, but somehow a quantity has already reached it, how? i thought it was counter intuitive. However, matt grime showed me how ignorant i was. It was just the way our number system has been stuctured. For example, i seemed to have a problem with 0.3333333 meters a second, but i had no problem with 1/3 meters a second. If you get what i mean...i guess what i just said had no point..

And another thing, It amazes me how The Tree is familiar with The Riemann Zeta Function, but not differentiating using the chain rule with a factor of 5 thrown in. Not taking a go at you or anything, but im assuming then your mathematical learning is off the internet and not from skool/textbooks? Good on you man, working independently, but seriously get some textbooks and itll help you ALOT. good luck

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O, and another thing that seems to give me a headache, why is the Riemann Zeta function called a function when it clearly gives more than 1 y value over the critical strip? am i missing something here?

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O, and another thing that seems to give me a headache, why is the Riemann Zeta function called a function when it clearly gives more than 1 y value over the critical strip? am i missing something here?

I don´t know the function so perhaps you should give some additional information. How is it obvious that there´s more than one f(z) for a given z? Did you possibly mistake the plot The Tree posted for an "f(x) over x" one? Judging from the labels I´d assume it is the complex values of the line f(x) : x -> Complex, f(x) = Riemann(1/2 + i*x) for x in some interval [x0,x1].

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O crap! thanks atheist, i did mistaken it for f(z) by z..my bad..and i just remember what the real function looks like, sorta like a hyperbola..my bad..

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• 1 month later...

my friend kept on saying that .999 equaled 1 in school and wouldnt be quiet about it... now i know where he got it from

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There is already a thread on this subject that was created over a year ago. bascule, you can check it out if you want to.

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my friend kept on saying that .999 equaled 1 in school and wouldnt be quiet about it... now i know where he got it from
No you don't. It's demonstrated all over the place, he could have got it from anywhere. From a text-book, the Internet, his teacher, a family member, worked it out himself, some kind of incredibly trivial maths journal... lot's of places.

Edit, and .999 isn't equal to one, 0.999... is. The difference is quite important.

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Ahh thats just nit picking, you knew perfectly well what he ment.

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Edit, and .999 isn't equal to one, 0.999... is.

Is what?

I see two things wrong with saying "0.999... is equal to one". Nothing wrong with saying 'equals'. The two problems:

• Use of the passive voice. One should say "0.999... equals one" instead.
• Not strong enough. Even better stated as $0.999... \equiv 1$, or in active English, "0.999... equals one, identically".

Saying "0.999 is one" still uses the passive voice and uses a word I can't find in my mathematical dictionary (i.e., "is").

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I seem to remember a long time ago me and matt grime were having an argument on this same subject, but more specifically on its relation to the physical world. I said how would it be possible to have in physical existance a quantity that had a non-terminating decimal expansion. I thought it would be impossible, because how could some quantity, which exists, be a value which never terminates, if u get wat i mean? like, the decimals go on forever, but somehow a quantity has already reached it, how? i thought it was counter intuitive. However, matt grime showed me how ignorant i was. It was just the way our number system has been stuctured. For example, i seemed to have a problem with 0.3333333 meters a second, but i had no problem with 1/3 meters a second. If you get what i mean...i guess what i just said had no point..

I had the same problem. I had to let go that it's just a system. 0.999... if expressed with infinite decimals would never reach 1, kind of limiting the system. I think it's intuitive that things have to end therefore you would expect the expression to end, I guess.

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Is what?

I see two things wrong with saying "0.999... is equal to one". Nothing wrong with saying 'equals'. The two problems:

• Use of the passive voice. One should say "0.999... equals one" instead.
• Not strong enough. Even better stated as $0.999... \equiv 1$, or in active English, "0.999... equals one, identically".

Saying "0.999 is one" still uses the passive voice and uses a word I can't find in my mathematical dictionary (i.e., "is").

it means exactly the same. who gives a damn.

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It's not the passive voice, although I can see where you're coming from. point-nine-recuring is the subject, and one is the noun so the action (of being equal) is being committed by the point-nine-recuring.

Of course equals doesn't really cover it, is identical to is a much better phrase because it emphasises that they are actually the same number.

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