Very easy problem that i dont understand

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The discussion centers on the relationship between the positive integer m and the variable r, expressed as m = 12r. It is argued that r must be an integer to ensure m remains a positive integer, as non-integer values for r could lead to m not being an integer. However, another viewpoint suggests that r can take on fractional values, such as 1/2 or 1/3, which would still result in m being a positive integer. The conversation highlights the importance of understanding the properties of number sets, particularly integers and their closure under multiplication. Ultimately, the necessity of r being an integer is debated, emphasizing the need for clarity in the original text regarding this mathematical relationship.
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m is a positive integer m = 12r

so r must be positive and an integer

why must r be an integer?
 
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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).
 
Blackwolf189 said:
m is a positive integer m = 12r
so r must be positive and an integer
why must r be an integer?

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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