Question

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

Answer 1

open.

Answer 2

really?

Answer 3

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

Answer 4

hmm...
what do you think sat?

Answer 5

i think it is neither

Answer 6

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

Answer 7

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

Answer 8

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...

Answer 9

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

Answer 10

I am looking a Leithold calculus and wikipedia

Answer 11

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

Answer 12

yes, and the endpoint is included

Answer 13

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

Answer 14

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

Answer 15

- 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

Answer 16

...didn't know that until yesterday

Answer 17

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

Answer 18

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.

Answer 19

Exactly @sat.

Answer 20

@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?

Answer 21

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

Answer 22

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

Answer 23

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.

Answer 24

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

Answer 25

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

Answer 26

so the interval is closed

Answer 27

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

Answer 28

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