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Do you only have properties about supremum?

I'll just take a picture of the prompt itself: http://i.imgur.com/2t9ecac.png

(I): http://i.imgur.com/VgX6bDE.png
Theorem 1.1.3.) http://i.imgur.com/w3awxCe.png

|dw:1441571930772:dw|

nah, I am only talking about the numbers between [ ]
I am just saying that [2,5] becomes [-5,-2]

-[a,b]=[-b,-a]

yes, but \(-\mathbb{R}=\mathbb{R}\)

\[-(-\infty, \infty)=(-\infty, \infty)\]

There is no point in doing this unless you are bounded above or below or both..

correct, you can think of it as a mapping, but you are just flipping it

I would write the set you suggested as \[\{-x\mid x\in \mathbb{R}\}\]

you dont graph sets.

Why not?

um, you graph relations

do you mean fill in the real line?

if X is the cup right side up, then -X is the cup upside down.

we are simply saying that if the set has an order, and we flip the set, then the order gets reversed

agreed

Alright. I can go with that. So, now the other questions.

I think if we get through the other stuff, this earlier stuff will be more clear.

And I know this is confusing :) it is the most failed class where I teach.

what do you mean by complete?

That is no longer real analysis, it would be on the "extended reals"

@Mendicant_Bias you still here?

http://i.imgur.com/zx2C0u0.png

ok, yes. This is the same comlete

do you just want to know the answer to part a?

when I say it must be in the set, I mean the universal set...

*universal set, not infinite set

but your answer says no next to infinity

Alright, I'll ignore the book question for now, maybe that was just bad writing?

It just says it is a set or real numbers, not THE set of real numbers.

Alright, that makes far more sense. So it was just me misreading the set notation.

Oh, such that

Just to let you know, I got to go pretty soon.