Another simple question.

[Rainbow]

Main Question or Discussion Point

My question is simple,

What is INFINITY?

How big or small is it?

What does one mean when he/she says that something(generally a physical quantity) is infinite?

Please help me with this.

 

[amcavoy]

It's more of a concept rather than a number. So when you say "infinite," you can't really say how large it is.

 

[Hurkyl]

http://en.wikipedia.org/wiki/Extended_real_number_line

 

[quasar987]

My question is simple,

What is INFINITY?

How big or small is it?

It's bigger than that.

 

[hypermorphism]

My question is simple,

What is INFINITY?

How big or small is it?

What does one mean when he/she says that something(generally a physical quantity) is infinite?

Please help me with this.

Infinity generally refers to a quantity that is without bound, ie., it is greater than all finite quantities. For example, the amount of natural numbers in the set of natural numbers is infinite because if the amount was a natural number, one could always find a natural number greater than that number by adding 1 to your number, contradicting the hypothesis that the amount is a natural number.
When referring to the "size" of an infinite set, one must then define how one wants to measure "size". For example, the set of all real numbers in the unit interval [0,1] is infinite but the interval [0,2] is larger than [0,1]. That's one way. But there is a problem. If you let f(x)=2x, you not only get f([0,1]) = [0,2], but each element in [0,1] is associated with a unique element in [0,2], giving the impression that [0,1] and [0,2] somehow have the same amount of elements. This is another measure of size called cardinality.
When one says a physical quantity is infinite, one is usually referring to a mathematical abstraction of the quantity, ie., slope, density, etc. It is usually a place in the equations where the theory breaks down and one relies on intuition to associate the infinity with a physical situation.

 

[Hurkyl]

Infinity generally refers to a quantity that is without bound, ie., it is greater than all finite quantities.

Those two phrases are not synonymous: any quantity serves as its own bound (both upper and lower bound). :tongue2:


I should point out that the +∞ and -∞ one sees in analysis (and thus in physics) has absolutely nothing to do with sizes of sets.