Infinity: a concept or number?

[Whovian]

However, with the exception of complex numbers, all "numbers" have a fixed location on a number line infinity does not. So, a concept of limitlessness.

Sort of how it's defined in Calculus. If a limit to a real number of a function grows without bound, we call it "infinity." Same goes for a limit to infinity, but a limit to infinity is as a number grows without bound.

 

[micromass]

I was told that Cantor possibly Hilbert as well, considered infinity to be a number. Is this true?

No, this is not true. Unless you can come up with a citation.

So infinity is a number then?

Did you not read my entire post?? There is no such thing as a number.

 

[micromass]

Is there any official mathematical dictionaries that define infinity? It seems to me that there are various views on this topic. Is there any authority that decides such things?

There is also no such thing as "infinity". There are various interpretations of infinity throughout mathematics. There are ordinals, cardinals, extended reals, projective spaces, etc. These are all incarnations of infinity.

 

[Hitarth]

Infinity is not a real number then why sometime it is domain or range of a real function?

 

[Whovian]

Infinity is not a real number then why sometime it is domain or range of a real function?

It isn't truly in any domain or range. A range of something like (0,∞) means that the range of the function has no upper limit, not that the upper bound is ∞.

 

[micromass]

Indeed, things like [x,+\infty) only have real numbers has elements. So infinity is not a member of the set. Furthermore, the notation "+\infty" is nothing more than a notation. It is a notation for

[x,+\infty) = \{y\in \mathbb{R}~\vert~x\leq y\}

If you don't like the infinity, then other notations are

[x,\rightarrow )~\text{or}~\uparrow x

 

[Number Nine]

So you consider infinity to be a number?

...as part of what set? With what operations?

 

[Diffy]

I don't understand why people on this forum respond the way they do to questions like these.

People asking these types of questions have little to no mathematical training. Trying to explain something like the extended reals to them just confuses the matter doesn't it?

Can we just assume these people are talking about the Reals? Simply because they obviously haven't studied or heard of anything else? Can't we just assume the question is "Is infinity in the Real number system?"

This way when someone asks this question, we can simply say: NO.

I really hate these threads, that are posted so often. And even when linked to the FAQ, the OPs don't read it.

Can we lock this? There is no math in it.

 

[micromass]

Can we lock this? There is no math in it.

Agreed.