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Munku you are confused on what r means.
r just means that digit repeats into infinity.
so if i have .99999999999999999999999999999999999...
and i multiply by 10 i get 9.99999999999999999999999999999...
so in this proof you say
x=.9r multiplying both sides by 19 gets us
10x=9.9r subtracting x from both sides gets us
9x=9.9r-x substituting .9r in for the second x gets us
9x=9.9r-.9r then 9.9r-.9r=9 (remember r is not a variable it is just a repeating of digits)
9x=9
x=1
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