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

- Thread starter syukai
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- #1

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

- #2

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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)

- #3

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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. :)

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

- #5

cristo

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In general, I'd say yes. But, it's normally easier to write something like [itex]x\in\mathbb{R}[/itex]Does ]-∞, ∞[ (can also be written as -∞<x<∞) mean all real numbers?

- #6

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Must be, in the US we typically use () to show open, and [] to show closed.I think the ] [ notation is used in other countries other than US.

- #7

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

- #8

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- #9

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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 [itex]x \in ]-∞, ∞[ [/itex]. You are right that ]-∞, ∞[ is all the real numbers, but an interval is defined from the real numbers, so that notation is rarely used.

- #10

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

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 [itex]x \in ]-∞, ∞[ [/itex]. You are right that ]-∞, ∞[ is all the real numbers, but an interval is defined from the real numbers, so that notation is rarely used.

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

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