Simple sup and inf questions

1. Oct 11, 2013

converting1

find the sup and inf of the following sets:

$${ x | x^2 - 5x + 6 < 0 }$$

I got the inf and sup to be 2 and 3 respectively

$${ x^2 - 5x + 6 | x \in ℝ}$$
here I was rather confused what this is saying. I'm assuming it's taking about the graph x^2 - 5x + 6 and assumed this was between [-1/4, ∞] so inf = -1/4 and sup does not exist as it is not bounded from above.

$${x | x^2 + 1 = 0 }$$
as I'm in a real analysis class, there isn't a real number such that x^2 + 1 = 0, so inf and sup do not exist

could anyone check my answers and if my reasoning is correct, especially for the second one please

I don't understand why the curly brackets are not showing, but there should be curly brackets around all above in tex

2. Oct 11, 2013

LCKurtz

Looks good.

It's talking about the range, so yes, that looks right too.

The curly brackets have a special use in TeX, so to display then you use \{ and \} as I did editing your first set.

3. Oct 11, 2013

converting1

thank you for a fast reply,

is the last one correct too as you did not comment on that?

4. Oct 11, 2013

LCKurtz

I would say so as long as your text doesn't have some special convention for empty sets.