# 1 = 0.999? How can you prove that 1 = 0.999999999999999999....?

(1) You might also consider that 1/3+1/3+1/3=1 or .333333...+.33333...+.33333...=1.

Note that we are saying that .99999...=1 exactly, not approximately.

You will encounter other proofs using other ideas as you go through school: the sum of an infinite series, the limit of an infinite sequence, etc...

If you disagree that .99999999....=1,...

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(1) You might also consider that 1/3+1/3+1/3=1 or .333333...+.33333...+.33333...=1.

Note that we are saying that .99999...=1 exactly, not approximately.

You will encounter other proofs using other ideas as you go through school: the sum of an infinite series, the limit of an infinite sequence, etc...

If you disagree that .99999999....=1, you have some company in the math world, though not much. Look up infinitesimals and you will find a fascinating history of a school of thought that differs from mainstream mathematics.

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Try this:

0.9999... /= 1

x=0.9999...

10x = 9.9999...

10x-x=9.0...

10x = 9+x = 9.999...

10x - x = 9.9999... - 0.9999...

the next line  9x=9 does not follow. It should be

10x = 9.999....

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1 is .99 rounded.  The more nines you get, the closer to one you will be.  However, 1 will never exactly each 0.99999999, no matter how many nines you add.  You will get closer and closer until the differnece is so minimal that you decide to call it 1.

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