m is a positive integer m = 12r
so r must be positive and an integer
why must r be an integer?
I think that they are claiming r to be an integer, to guarantee that m is an integer. I'm not sure what the else the question/statement says, but that's what I believe they're getting across.
furthermore, I think the text is trying to focus on certain "main" number sets. I.e. integers, rationals, irrationals, etc. So they say r is an integer. If r is not an integer, and say irrational, then of course m would not necessarily be an integral number>0. Simply put, the integers is the only safe-bet for r to belong to, so that m is positive and greater than zero (for all r in the set).
It doesn't, it might be 1/2, 1/3, 1/4, 1/6, or even 1/12. All of those make m a positive integer. Of course, the other way is true: IF r is an integer then m must be- the integers are "closed" under multiplication. Exactly what did the book you got this from say?
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