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Simple sup and inf questions

  • #1
find the sup and inf of the following sets:

[tex] { x | x^2 - 5x + 6 < 0 } [/tex]

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

[tex] { x^2 - 5x + 6 | x \in ℝ} [/tex]
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.

[tex] {x | x^2 + 1 = 0 } [/tex]
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
 

Answers and Replies

  • #2
LCKurtz
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find the sup and inf of the following sets:

[tex] \{ x | x^2 - 5x + 6 < 0 \} [/tex]

I got the inf and sup to be 2 and 3 respectively
Looks good.

[tex] { x^2 - 5x + 6 | x \in ℝ} [/tex]
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.

[tex] {x | x^2 + 1 = 0 } [/tex]
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.
 
  • #3
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?
 
  • #4
LCKurtz
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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.
 
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