(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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what do you do for a living and how old are you

It's not working for me anymore either. Would you mind deleting the thread until I sort things out?

EDIT: Fixed (I hope).

If decimals were 100% accurate, you wouldn't have gotten your answer that .99999=1. And(I'm smart) what do you do for a living and how old are you?

What are you basing this on? You can't just make arbitrary claims and state that they are fact.

My age and occupation have nothing to do with the accuracy of decimals.

Also, you clearly aren't "smart." You thought the error in my last thread was due to setting both variables equal to the same value :derp:.

Haha you're wrong buddy. Re-read the problem.

One third is equal to 0.33333...

Three times one third is equal to 1:

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

Therefore 1=0.999999...

---------- Post added at 10:01 PM ---------- Previous post was at 10:00 PM ----------



Works now

They aren't "arbitrary claims", they are fact. And(I'm smart) I was just asking what your occupation was because you seem to be very interested in math. And(I'm smart) where did I post in your last thread?


... seriously.

Why do you keep saying your smart?
You seem to be pretty cocky.