(adsbygoogle = window.adsbygoogle || []).push({}); I will prove that 1=0.999999... This one IS NOT a troll (no sneaky tricks like the last one i.e. dividing by zero).

The Fractions Proof

This one requires little to no math knowledge. Note that You must login or register to view this content. represents 0.999999...

One third is equal to 0.33333...

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Three times one third is equal to 1:

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Three times 0.33333... is equal to 0.999999...

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Therefore 1=0.999999...

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The Infinite Series Proof

A number with a repeating decimal can be represented as a sum of an infinite series:

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The formula to find the value of an infinite series where |r|<1 is as follows:

S is the sum, t1 is the first term in the series, and r is the rate.

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Therefore:

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The Algebraic Proof

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Multiply both sides by 10 (remember that when you multiply by ten it shifts the decimal place to the right by one place):

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Subtract x=0.9999... from both sides:

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Simplify:

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Divide by 9:

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The Midpoint Proof

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What is the midpoint (average) between a and b? The formula to find m where m is the midpoint is:

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Using the values for a and b:

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You can use long division to divide 1.9999... by 2 to get m=0.99999...

Since the midpoint between the two points IS one of the two points, the two points MUST be equal. If you are unconvinced that this is true, you could say from the information that:

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Multiply both sides by two:

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Subtract b from both sides:

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Simplify:

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Substituting numerical values:

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you sir a freaky mathematical devil

Its not, i just couldn't think of the right word to fit in there. xD

If he is trying to prove that 0.999=1 and he is using 0.333 his proof is inaccurate. 1 third is 0.3 followed by infinite threes, so the only way to prove what he is trying to prove is for him to use 0.333 followed by infinite zeroes or the fraction 1 over 3.

yo i straight suck in math lol

I DID use 0.3333 followed by infinite threes. What about this is complicated?

multiply 1/3 by 3 and 0.33 by 3 and tell me what u get? they are not the same
so now multiply 1 by 3 and 0.99 by 3, they are not the same
Therefore ur theory is wrong :p

HAHA for a second there, i actually agreed.

lol my head hurts ugh...