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Oh i love these brain exercises!

by 1+1=1
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1+1=1
#1
Jun20-04, 02:36 PM
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if x and y are pos. int. then rx >=y. x is an int. help!
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Gokul43201
#2
Jun20-04, 02:57 PM
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What is the question ?

If x, y are positive integers, there can always be found an r such that rx >= y. (Why repeat "x is an integer" ?) Do you want a proof of the above statement ?
Gokul43201
#3
Jun20-04, 03:05 PM
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Assume that y > rx , for all r

Then the set S = {y-rx| r in Z+} consists only of positive numbers. So, S must possess a least element, say y-mx.

But y-(m+1)x also belongs in S, since m+1 is in Z+ if m is.

y-(m+1)x = y-mx - x < y - mx, since x>0, contrary to our choice of the minimal element - a contradiction !

Hence, the assumption was false.


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