# Simple sup and inf questions

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

Homework Helper
Gold Member
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

Looks good.

$${ x^2 - 5x + 6 | x \in ℝ}$$
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.

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

$${x | x^2 + 1 = 0 }$$
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

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

converting1
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.

thank you for a fast reply,

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

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