Is Infinity a Concept or a Number?

[romsofia]

Hey, is infinity a concept or an actual number?

This is a discussion with someone, I say it's a concept but then he brought up set theory, and I have no set theory knowledge whatsoever.

 

[icystrike]

Infinity does not behave according to ur laws of arithmetic(usual number)...

1/0 = inf
1= inf * 0
1= inf*(0+0)
1=2 (contradiction)

 

[arildno]

What is a number?
Answer:
An element of a particular number system.

A number system is a set, where you have defined some operations, i.e, "stuff" you can "do" with your elements. For example, you might pick any two elements, and according to some specified procedure associate a third element to your picked pair of elements.
Typical examples of such operations are "addition" and "multiplication" (Pick two numbers, add them, and gain a third number).

Now, in our "ordinary" number systems, there is no element that reasonably could be called "infinite". Thus, within these number systems, infinity is not a number.

However, it is perfectly possible to construct number systems in which infinity is a number as well.

 

[micromass]

Well, the most disturbing thing about infinity is that there are many different forms of it. Sometimes it behaves as a number, sometimes as a concept...

Infinity as a number:
- Surreal numbers
- Hyperreal numbers
(in the real numbers, infinity is certainly not a number!)

Infinity as concept:
- cardinality
- limits

Infinity as "points in the space":
- one-point compactification
- ordinals and cardinals
- projective space

So there are many different flavours of infinity. So the original question is actually not correct, since there is no one thing called infinity. There are many different object which are all called infinity...

 

[Robinsmermaid]

Well, the most disturbing thing about infinity is that there are many different forms of it. Sometimes it behaves as a number, sometimes as a concept...

Infinity as a number:
- Surreal numbers
- Hyperreal numbers
(in the real numbers, infinity is certainly not a number!)

Infinity as concept:
- cardinality
- limits

Infinity as "points in the space":
- one-point compactification
- ordinals and cardinals
- projective space

So there are many different flavours of infinity. So the original question is actually not correct, since there is no one thing called infinity. There are many different object which are all called infinity...

Wow I have been trying to explain what you just said!