B bearej50 New member Joined Feb 16, 2009 Messages 21 Feb 23, 2009 #1 (a) Prove: If y > 0, then there exists n ? N such that n-1 < y < n. (b) Prove that the n in part (a) is unique. I have already proved part (a). I am having difficulty with the part (b). Thank you in advance.
(a) Prove: If y > 0, then there exists n ? N such that n-1 < y < n. (b) Prove that the n in part (a) is unique. I have already proved part (a). I am having difficulty with the part (b). Thank you in advance.
D daon Senior Member Joined Jan 27, 2006 Messages 1,284 Feb 23, 2009 #2 Re: Real Analysis Assume n-1 <= y < n and m-1 <= y < m and n is not equal to m. Then (n-1)-(m-1) <= y-y < n-m => (n-m) <= 0 < (n-m), which violates the trichotomy for real numbers. Therefore m=n.
Re: Real Analysis Assume n-1 <= y < n and m-1 <= y < m and n is not equal to m. Then (n-1)-(m-1) <= y-y < n-m => (n-m) <= 0 < (n-m), which violates the trichotomy for real numbers. Therefore m=n.
