Mathematics

Question

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

1 Answer

  • No.  We claim that [tex]1=0.\overline{9}[/tex] and use algebra to prove the statement.

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