Question

Consider the set S of real numbers in which the hundreths digit in its decimal expansion is equal to 3. Is S a finite, countably infinite, or uncountable set? Prove your claim

Answer 1

? what difference does it make if there is a 3 in the hundredth digit?

Answer 2

map your set on to the real numbers by removing the 100th digit and shifting every thing after one place left. still get all the reals

Answer 3

so is it uncountable