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## Homework Statement

34) Determine whether each of these sets is countable or uncountable. For those that are countable, exhibit a one-to-one correspondence between the set of natural numbers and that set.

a) integers not divisible by 3

b) integers divisible by 5 but not by 7

c) the real numbers with decimal representations consisting of all 1s

d) the real numbers with decimal representations of all 1s or 9s

## Homework Equations

N = {0, 1, 2, 3, ...}

## The Attempt at a Solution

Not a clue where to start.

For a), how do I express something as divisible by 3? It is either:

Divisible by 3

A number divisible by 3, + 2, or..

A number divisible by 3, + 1.

b) is the same as a), just worse.

c), this would have something to do with the fraction 1/9.

d), same as c), only includes the 9s too. Unsure what fraction gives 9s (Unless 9/9, as people say that 1 = 0.9999... *Shrug*)