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Mathematics
OpenStudy (turingtest):

quick! [0,+infty) open or closed interval?

OpenStudy (anonymous):

open.

OpenStudy (anonymous):

really?

OpenStudy (anonymous):

Waiit. Open at the right end. Closed on the left.

OpenStudy (turingtest):

hmm... what do you think sat?

OpenStudy (anonymous):

i think it is neither

OpenStudy (anonymous):

although perhaps it depends on the definition complement is open, so pehaps we should say closed

OpenStudy (anonymous):

i am going to change my vote to closed, since compliment is open, which is usually the definiton of closed

OpenStudy (turingtest):

I got a few contradictory bits of info, but my understanding is that the interval is closed if it includes its extrema extrema have to be real numbers, and since the only real number in [0,+infty) is 0, it is closed however wikipedia says something a little vague...

OpenStudy (anonymous):

No. http://mathworld.wolfram.com/OpenInterval.html

OpenStudy (turingtest):

I am looking a Leithold calculus and wikipedia

OpenStudy (anonymous):

It's likif the end point is included - Its closed. If the end point is excluded- It's open.

OpenStudy (anonymous):

yes, and the endpoint is included

OpenStudy (turingtest):

and infinity is not a point, so that messes the whole thing up

OpenStudy (anonymous):

so i guess another way to say this is that \[[0\infty)\] incudes its limit points

OpenStudy (turingtest):

- Equivalently, a set is closed if and only if it contains all of its limit points. - Half-interval [1, +∞) is closed. source:wikipedia http://en.wikipedia.org/wiki/Closed_set plus, as I said, it saus closed in my Calc book

OpenStudy (turingtest):

...didn't know that until yesterday

OpenStudy (anonymous):

not to fret about the infinity part, because infinity is not a number, so it is not the limit of anything

OpenStudy (anonymous):

Hmmm. Yes. Infinity is just a way of saying that it goes upto well, all numbers on the number line. So it's not a point. Including it wold be considering an end. I think.

OpenStudy (anonymous):

Exactly @sat.

OpenStudy (turingtest):

@satellite73 what do you mean infinity is not the limit of anything? the limit as x goes to infinity of f(x)=x=infty so it's the limit of something, no?

OpenStudy (amistre64):

infinity is more of a direction i beleive; even tho there are different sets of infinity that do not contain the same cardinality\[\aleph _0 < \aleph _1\] i hope that shows up lol

OpenStudy (turingtest):

no, not yet I think they are rebooting latex but I think this infinity is a continuum infinity since it is not countable (it's a line) not that that makes a difference here

OpenStudy (anonymous):

x goes to infinity. You aren't limiting it, are you. You are saying that it goes on the right hand direction on the numberline forever.

OpenStudy (turingtest):

but you still say that "the limit is infinity" hence, the limit exists, and it is infinity

OpenStudy (turingtest):

that is different then the limit of x to infinity of sinx, which has no limit at all

OpenStudy (turingtest):

so the interval is closed

OpenStudy (anonymous):

You don't say limit is infinity. You say x approaches infinity.

OpenStudy (turingtest):

infinity is defined in terms of limits, it has no meaning by itself infinity is defined as lim x->infty f(x)=x, or lim x->0 1/x (or some limit that converges to infinity) hence our interval can written [a,+infty)=[a, lim x -> infty x) whatever x approaches such that the function approaches infinity is irrelevant

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