Need help with integral notation (algebra related).?

Question

I'm slightly confused with integral notation. I understand it for the most part but I don't quite understand infinity.

Let's say I have x>5. The first part is ( because it doesn't touch five. The second part is infinity. Now I'm having trouble closing it off. So it's (5, oo ?

In all the problems I have, it's always closed off with a circular bracket. But since all the numbers of infinity ARE INCLUDED, shouldn't it end with a ] ?

Answer 1

You're speaking of Interval notation (not integral notation).

There's no such thing as "all the numbers of infinity." The idea is that you use a bracket "]" when you _include_ the number on that end. Infinity is not a numbers; it's simply the concept of continuing to the theoretical end of the number line (which doesn't literally end).

Another way of looking at it is that ] is used on closed intervals, and ) is used on open intervals. An interval is closed if it has a definite stopping point, or if it has a "largest" element. On the interval (5 , oo ), there is no "largest" number, or definite stopping point. No matter what large number you pick in the interval, you can find a larger one.

Infinity (and negative infinity) is _always_ an open interval, so it _always_ uses parentheses ")" .

Answer 2

This is not INTEGRAL but INTERVAL notation :)

Infinity is not a number, but "something" that is greater than any number. Therefore, you use the notation

5 < x < oo ... or ... (5, oo)

because x = oo is not possible if x is a number.

There are theories (e.g. measure and integration theory; or examples in topology on sets of cardinal numbers) in which a difference is made between (0, oo) and (0, oo].

Answer 3

infinity isn't a number, so you can't include it in your interval (by the by, "integral" is calculus). Therefore, your interval ends with a round bracket (5, oo).
"all the numbers of infinity".. How big is infinity? You can never reach it, so you can't include it. x>5 means x can be any of the numbers from, but not including, 5, up to as big a number as you like, i.e. "arbitrarily large".

Answer 4

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Answer 5

(5, oo ]