Hi

I was going through Cantor Second Diagonal Method. It pertains to proof that there are uncountable real numbers between 0 and 1.

Lets say x is a number such that ..

x = 0.a1 a2 a3 ... an .... (ak takes values between 0 and 9 both included)

I quite did not figure out why there is a condition on ak.

ak can't be 9 for all values greater than equal to n for some constt n.

A related question .. while i was trying to understand above mentioned theorem.

Lets say x= 0.199999999999999999.......ad infinitum

then 10x = 1.999999999999999.........ad infinitum

also 100x = 19.9999999999999999........ad infinitum

it implies 90x = 18

it implies x = 0.2

I CAN'T FIGURE THIS OUT..

SINCE 0.2 != 0.19999999999999.......ad infinitum

Plz help me understand this.