# Math Help - Finding the supremum and/or infimum of these sets.. (real analysis)

1. ## Finding the supremum and/or infimum of these sets.. (real analysis)

I've been working on real analysis for a short time and am really struggling to find the supremum and infimum of these sets (or if they exist at all)

the set of rational numbers in the interval [0,1]

the set of real numbers in the half open interval ]0,1]

the half line x ∈ R | x≤0

S={(x^2+y^2/xy)|x>0, y>0}

thank you!

2. ## Re: Finding the supremum and/or infimum of these sets.. (real analysis)

Originally Posted by kaya2345
I've been working on real analysis for a short time and am really struggling to find the supremum and infimum of these sets (or if they exist at all)
the set of rational numbers in the interval [0,1]
the set of real numbers in the half open interval ]0,1]

the half line x ∈ R | x≤0

S={(x^2+y^2/xy)|x>0, y>0}
The first two have both inf & sup. And they are the same for both set.

The third has only sup.

For the fourth, is that the same as $\frac{x}{y}+\frac{y}{x}~?$

3. ## Re: Finding the supremum and/or infimum of these sets.. (real analysis)

Originally Posted by Plato
The first two have both inf & sup. And they are the same for both set.

The third has only sup.

For the fourth, is that the same as $\frac{x}{y}+\frac{y}{x}~?$
thank you for that do the first two have both because they're rational and real? would it not be different for the half open interval?

and yes the fourth is the same as x/y + y/x

4. ## Re: Finding the supremum and/or infimum of these sets.. (real analysis)

Originally Posted by kaya2345
thank you for that do the first two have both because they're rational and real? would it not be different for the half open interval?

and yes the fourth is the same as x/y + y/x

NO. $\inf(0,1]=0~\&~\inf[0,1]=0$.