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.
