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What I think is that since every countable set C ~ Z+( all positive integers) and Z+ is infinite, then C is also infinite. Sounds straightfoward but I need to check it.

Thanks,

Ronn

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- Thread starter Ronn
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- #1

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What I think is that since every countable set C ~ Z+( all positive integers) and Z+ is infinite, then C is also infinite. Sounds straightfoward but I need to check it.

Thanks,

Ronn

- #2

HallsofIvy

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Be aware, however, that some books use the term "countable" to include finite sets- defining countable to mean there is a one-to-one function from the set

- #3

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1. If A is a subset of B and B is countable, then A is at most countable?

If 1 is correct, then A is either finite or countable by definition.

2. What if A is known to be infinite,then is it safe to say A is countable? i.e., Since A is either finite or countable, if A is infinite it is the other case where A is countable.

Thanks again!

Ronn

- #4

Dick

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