- #1
Felafel
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Homework Statement
Hello. I think I've managed to solve the exercise, but I'd like it to be checked and I'd also like to kow whether it is well-written and explained enough.
The problem is: find the supremum and infimum of this set:
[itex] A= \{ \frac{m}{n}+4\frac{m}{n} : m,n \in \mathbb{N}^*\} [/itex]
The Attempt at a Solution
if m=n then 5 is the only element of the set. Therefore it is its minimum and maximum and also its supremum and infimum.
if m<n the infimum (and also the minimum) is ## \frac{17}{2} ## because the minimum values for m and n are 1 e 2.
if n<m the infimum is 4, for the same reason.
either when m<n or n<m the supremum is ## +\infty ##