(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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Haha Main word being somehow.

You aren't telling us anything new. 0.999... equalling 1 is taught in textbooks.

I see how it works, but i still disagree. 0.99999... = 0.99999...
..... Sorry, i guess its just a matter of opinion. :/

Your right. It is what it is but it is just shy of 1, not exactly one.

You are right, 0.9999999999 = 1

But this isn't denied or anything. Go to your calculator and type 0.9999999999 then press = , the result will be 1.

Same to any number , I.E 9.999999999= 10.

Let's say 9.9 = 99 over 100 so when the decimal increases 99 will be approximated to 100 so it will be 100 over 10 so a zero will be cancel so it's equal 10.

Because(I'm smart) Dopey said if you use a conjunction at the beginning of a sentence, it makes you smart.

Sorry but how is math an OPINION?

1. Yes they are arbitrary claims. You claim that decimals aren't accurate. That doesn't make any sense - decimals are just as accurate as we make them. It's like saying that integers aren't completely accurate - it just makes no contextual sense.

2. In my previous thread, you said: "'a' and 'b' both can't equal 1"

I responded sarcastically, saying that you should win the Fields Medal.



"Because" isn't a conjunction.



It isn't opinion. I gave four different proofs that 1=0.99999...

It doesn't matter whether or not you agree, it is what it is.



Incorrect, it is exactly =1. Think of it this way:

What is the difference between 1 and 0.99999... ? The difference is 0.00000000...1, with an infinite amount of zeros preceding the 1. Since there is an INFINITE amount of zeros, the 1 will never be added to the end.



That's because the calculator rounds the result. I'm showing that 0.9999... isn't APPROXIMATELY =1, it is EXACTLY =1.



Correct. Any number with infinitely repeating 9's in the decimal place will be equal to the integer preceding the decimal place +1.



I'm not doing any approximations. I'm showing that it is EXACTLY =1.

Learnt the algebra way today in Maths