Integer Proof
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I am stuck at this question in my hw. It seems very very familiar, but sumhow I dunno how to do it.
The fractional part of x is the amount by which it exceeds its floor, [x]. For
x in R (real number system) and n in N(integer), let S={x,2x,...,(n-1)x}.
a) Prove that is some pair of numbers in S have fractional parts that differ by at most 1/n, then some number in S is within 1/n of an integer.
b) Use part a to prove that some number in S is within 1/n of an integer.
Any help appreciated
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Wah! Looked like something I'm learning now....
Hmmm....no idea leh.
Hmmm.....prove by contradiction?
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My TA gave me what she called a big hint this afternoonOriginally posted by CoolMyth:Wah! Looked like something I'm learning now....
Hmmm....no idea leh.
Hmmm.....prove by contradiction?
Supposed to be solved by using Pigeonhole principle... -
Pigeonhole ah....Originally posted by rainee:My TA gave me what she called a big hint this afternoon
Supposed to be solved by using Pigeonhole principle...
That one I not very good at using. Sorry, like to help but I'm too lousy....
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it is alrite, I learn abt pigeonhole like 2 years ago and now I cant remember how it really works le...Originally posted by CoolMyth:Pigeonhole ah....
That one I not very good at using. Sorry, like to help but I'm too lousy....
will go and read up on it later