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Homework Statement
What is the cardinality of the set of all numbers in the interval [0, 1] which
have decimal expansions with a finite number of non-zero digits?
Homework Equations
The Attempt at a Solution
I say its still c? Am I correct, there is no way I can pair this set with the natural numbers.
Define
f(1) = 0.1
f(2) = 0.02
f(3) = 0.003
f(4) = 0.0004
...
But then we must pair elements of N to 0.2, 0.3, 0.4... and 0.03, 0.04, 0.05, and 0.004, 0.005,...
This seems weak though no?
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