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Old 09-09-2006, 04:34 PM   #220
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Originally Posted by cookiemonster
You're wrong. They are EXACTLY equal BY DEFINITION. 9.99999999... is just another way of writing 1.

It is simple to prove this by contradiction.

Suppose it is not exactly equal to 1, that they're two separate numbers.

Let a=.9999..... b=1
Since the space of real numbers is compact is a compact set, there exists by neccessity a number c between 9.9999... and 1. a<c<b (strict inequality)

Yet, for any number c that you chose, c<a

Therefore, we have a contradiction... this implies that a=b.
Trust me...I have tried that
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