how the set of integers divisible by 7 becomes finite
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have searched for the answer to this question online and have come across some answers, however, I am struggling to understand it. How would I come up with a function for which the integers are multiples of 5 but not multiples of 7? I also want to show a one-to-one correspondence with the set of positive integers, so that I can prove it is countably infinite. This is what I have so far:
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it is countable by finding a one-to-one onto correspondence as follows:
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