Very easy problem that i dont understand

  • Context: High School 
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Discussion Overview

The discussion revolves around the conditions under which the expression m = 12r results in m being a positive integer. Participants explore the implications of r being an integer and the potential for r to take on other values.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants propose that r must be an integer to ensure that m is an integer, as this aligns with the properties of integer multiplication.
  • Others argue that r does not necessarily have to be an integer, suggesting that fractional values such as 1/2 or 1/3 could also yield a positive integer for m.
  • A participant mentions that the text may be emphasizing specific number sets, indicating that if r were irrational, m would not be guaranteed to be a positive integer.
  • One participant questions the original statement, asking for clarification on what the source material claims regarding the relationship between r and m.

Areas of Agreement / Disagreement

Participants express differing views on whether r must be an integer, with no consensus reached on the necessity of this condition for m to be a positive integer.

Contextual Notes

The discussion highlights the dependence on definitions of number sets and the implications of r's value on m, but does not resolve the mathematical steps or assumptions involved.

Blackwolf189
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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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