Real Analysis:If y>0, there exists natural n s.t. n-1<y<n

[bearej50]

(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.

 

[daon]

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.

 

[bearej50]

thank you greatly