(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...

You must login or register to view this content.

Three times one third is equal to 1:

You must login or register to view this content.

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

You must login or register to view this content.

Therefore 1=0.999999...

You must login or register to view this content.



The Infinite Series Proof

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

You must login or register to view this content.

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.

You must login or register to view this content.

Therefore:

You must login or register to view this content.



The Algebraic Proof

You must login or register to view this content.

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

You must login or register to view this content.

Subtract x=0.9999... from both sides:

You must login or register to view this content.

Simplify:

You must login or register to view this content.

Divide by 9:

You must login or register to view this content.



The Midpoint Proof

You must login or register to view this content.
You must login or register to view this content.

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

You must login or register to view this content.

Using the values for a and b:

You must login or register to view this content.

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:

You must login or register to view this content.

Multiply both sides by two:

You must login or register to view this content.

Subtract b from both sides:

You must login or register to view this content.

Simplify:

You must login or register to view this content.

Substituting numerical values:

You must login or register to view this content.

Yea I agree mate, 7th grade algebra can be a pain in the ass.

You see where you wrote now subtract x=0.99999 etc.
I think u subtracted wrong because the left side would be 9.0000001
Correct me if im wrong

Proof that anything = 0

0 x # = 0

You must login or register to view this content.[/QUOTE]

I spent an hour trying to find a way to argue against what you said without sounding like an uneducated idiot. I couldn't find a way.

The fraction example really hits home for me...

3 * 1/3 = 1; 1/3 + 1/3 + 1/3 = 3/3 = 1
1/3 = 0.333...; 3 * 0.333... = 0.333... + 0.333... + 0.333... = 0.999...

Therefore we can assume that 1 = 0.999...

wow thats pretty kool didnt know that

You can't divide by 0?
WHADDAF00K