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-BARSIC- [3]
3 years ago
7

Question: is 1 > 0.99999999...?Prove algebraically.

Mathematics
1 answer:
Crazy boy [7]3 years ago
6 0
No.  We claim that 1=0.\overline{9} and use algebra to prove the statement.

Let x=0.\overline{9}.  Multiply this by ten to get 10x=9.\overline{9}.  Subtract the initial equation to give 9x=9 and divide by 9 to see that x=1.  Substituting into the original equation gives 1=0.\overline{9}, proving the desired statement.
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