0.999... = 1

Mathematical proofs that 0.999... = 1.

Deal with it!

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• .999...

[madmatix]

Oh repeating decimals, they do go on forever...but we don't. 

[CousinoMacul]

@madmatix Recurring things and quotient rings make way for other joys.

[OhMyFreakingGoshh]

Not really; it just shows that 1 isn't divisible by 3 or any other number.

Because if what you say was accurate, that would mean we could do the exact same thing with "1/2 + 1/2 = 2/2 = 1" and get 0.999...

But if you try it you will get 0.888...

[CousinoMacul]

@OhMyFreakingGoshh Divisibility doesn't enter into this since we're talking about the real numbers, not the integers.

What you say about 1/2 is true in base 9 (in base 9, 0.888...=1), but in base 10, 1/2=0.5 is not a repeating decimal.

[utsudoshi]

Fraction form = rational

Decimal form = irrational

Irrational (does not) = rational

My beard is a windmill and your argument is invalid.

[CousinoMacul]

@utsudoshi Nope! Rational means it can be written as integer fraction. All repeating decimals are rational. Here's how to find their fraction: 1) Take repeating part 2) count how many digits it has (call that n) 3) divide by 10^n - 1 For example, 0.277277277... = 277/999 (999=10^3 - 1) Also, 0.19191919... = 19/99 And of course, 0.999... = 9/9 = 1 Try it out yourself on any repeating decimal if you don't believe me.

[Eyeodine]

I'll believe you when you can write .9999999.... to infinity. :)

[madmatix]

@CousinoMacul Joys?

[SketchyTree]

All this means is that you can translate a fraction into decimal form, but you cannot translate a decimal back into a fraction; something is lost in the process.

[1Guggaburggi]

This is fake! In your second proof:

If x=.9999....., then 10x is not 9.99999....

10x is 9.999999......0, zero from multiple must go to the end of digit.

[OhMyFreakingGoshh]

@CousinoMacul Base 9, Base 10? What's that? :S

[MarineFocus]

This guy just showed a couple of proofs. For those of you who disagrees, please stop acting you know everything and GTFO. Come back when you've taken first year university level math course.