Finding Sup and Inf in Real Analysis: x^2 - 5x + 6 < 0 and x^2 + 1 = 0

[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

 

[LCKurtz]

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?

 

[LCKurtz]

thank you for a fast reply,

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

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