1. ## find the infimum

inf{ z = x + x^(-1): x>0 }

any help would be greatly appreciated!

2. Originally Posted by pseudonym
in{ z = x + x^(-1): x>0 }

any help would be greatly appreciated!
What percisely are you having difficulties with?

3. Originally Posted by pseudonym
in{ z = x + x^(-1): x>0 }
For every $a~\&~b$ it follows that $a^2+b^2\ge 2ab.$.
Equality holds only if $a=b$

For your problem let $a=\sqrt{x}~\&~b=\frac{1}{\sqrt{x}}.$

4. Originally Posted by Drexel28
What percisely are you having difficulties with?

my understanding is that I have to find the greatest lower bound, i.e. the smallest value of x for z to exist?

5. Originally Posted by pseudonym
my understanding is that I have to find the greatest lower bound, i.e. the smallest value of x for z to exist?
Do you understand that every $z$ in your set is such that $z\ge 2?$