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- Thread starter GunnaSix
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Hurkyl

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Can you convince yourself that this conjecture is equivalent toI don't know if you can say that there are no irrational numbers in an infinite list of integers.

Every integer is rational

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are you talking of integer degrees or radians?

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SineX = 0 only where X = n*pi radians. But n*pi must be an irrational number or 0. Thus SineX is either greater than or less than 0 for any integer angle n in radians where n>0. I think this is what the poser was asking.

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HallsofIvy

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Yes, since any integer, n, can be written as the fraction n/1, all integers are rational numbers. There are no irrational integers. It is true that sin(n) is never 0 for any integer n- but that does NOT mean "greater than 0". sin(4) is negative.

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While I used the langauge "Sine x" is "greater than or less than 0", the poser asked whether "the absolute value of Sine x is greater than 0 for all integer values of x.". I think you had my language in mind when you overlook the "absolute value" part of the poser's question.Yes, since any integer, n, can be written as the fraction n/1, all integers are rational numbers. There are no irrational integers. It is true that sin(n) is never 0 for any integer n- but that does NOT mean "greater than 0". sin(4) is negative.