Is ]-∞, ∞[ the Same as All Real Numbers?

[syukai]

Does ]-∞, ∞[ (can also be written as -∞<x<∞) mean all real numbers?

 

[Diffy]

]-∞, ∞[

Never seen it written like that I would be more inclined to write :
[-∞, ∞] or more commonly me thinks (-∞, ∞) - to show that this is open

When you write -∞<x<∞ I guess the most common assumption is that x is contained in the reals but without context it really isn't smart to assume anything. Usually someone will specifically state x contained in the reals and -∞<x<∞ - or x contained in the integers and -∞<x<∞ or the set that x belongs to will be clear from the context.

(Sorry for not responding with yes or no but hopefully you understand why I could not)

 

[syukai]

If the brackets are facing outwards ][ then they're supposed to mean the points are excluded.
If the brackets are facing inwards [] then they're supposed to mean the points are included.
At least, that's what I was told, and that's what I read in my textbook.

Anyway, yes, I see your point. Another number with the answer of "all real numbers" simply showed the symbol for it, so I'm pretty wary of assuming that -∞<x<∞ means "all real numbers" as well.

Thank you for your input though. :)

 

[NoMoreExams]

I think the ] [ notation is used in other countries other than US.

 

[cristo]

Does ]-∞, ∞[ (can also be written as -∞<x<∞) mean all real numbers?

In general, I'd say yes. But, it's normally easier to write something like $x\in\mathbb{R}$

 

[Diffy]

I think the ] [ notation is used in other countries other than US.

Must be, in the US we typically use () to show open, and [] to show closed.

 

[ice109]

yes that's exactly what that notation means and pretty much the only legit use of the symbol ∞

 

[syukai]

Aaaah, thanks. I asked my math teacher before I read the last few posts, and confirmed that the answer is yes as well. :)

 

[mrandersdk]

You say

Does ]-∞, ∞[ (can also be written as -∞<x<∞) mean all real numbers?

first of all there is a difference between ]-∞, ∞[ and -∞<x<∞, the first is all the real numbers, the second is the same as $x \in ]-∞, ∞[$. You are right that ]-∞, ∞[ is all the real numbers, but an interval is defined from the real numbers, so that notation is rarely used.

 

[Diffy]

You say

Does ]-∞, ∞[ (can also be written as -∞<x<∞) mean all real numbers?

first of all there is a difference between ]-∞, ∞[ and -∞<x<∞, the first is all the real numbers, the second is the same as $x \in ]-∞, ∞[$. You are right that ]-∞, ∞[ is all the real numbers, but an interval is defined from the real numbers, so that notation is rarely used.

the itex tags are misrepresenting your point. I view it as x in ] -8743, 8743 [

But what you actially wrote was x \in ]-∞, ∞ [ with itex tags.