I'll tell you why it should be outlawed: Because it doesen't exist, anywhere. Everything in the Universe has a limit. From the number of molecules on the Earth to the number of stars in the Galaxy. Sure the number is larger than any number we can probably comprehend, but there IS a limit.

Can anyone give me an example of something that is REALLY infinite, besides a stupid symbol that we came up with?

What about Pi. No one has yet found an end to it. I think Phi is the same way too.

I'm not talking about numbers here.
So I don't want to hear about PI, PHI, the set of natural numbers, the set of integers, I'm talking about things in NATURE, not measurements. I'm talking about things you can touch and see.

You CAN see Phi in nature. It's the spiral of sea shells and rows of seeds in a sunflower, the arangment of petals in a flower, the placement of stems on a branch.

When then you don't really understand what 'infinity' is used for. It's obviously not something you can touch.

No, that doesn't mean it doesn't exist. It just means that you couldn't prove it.

There are discrete things in nature. Every discrete thing has a boundry. A boundry is infinitely thin. Welcome to one of the many magical uses for infinity.

This is a math forum. whether infinity actually exists as something you can see doesn't really matter. NEITHER DOES ZERO. Both are intertwined and the basis of ost technologies we have today.

So please shut off your computer and burn it... as you are using a technology that was developed using the concept of infinity... and it is now outlawed.

You CAN see Phi in nature. It's the spiral of sea shells and rows of seeds in a sunflower, the arangment of petals in a flower, the placement of stems on a branch.Well, you can see a fairly good approximation. You don't actually have the number PHI... just something insanly close.

I'll tell you why it should be outlawed: Because it doesn't exist, anywhere.
So what? Should all concepts without a physical analog comprehensible to you be outlawed?

Infinity is a mathematical entity. It exists independently of the Universe.

I suppose you'd also like to outlaw i? How about 0? -1?

Infinity is useful when you're in the regime of "this is much much much bigger than this" to the point of being infinite. It makes for really nice physical approximations, too. The fact that you've never seen these approximations, or tried to work out the results without them, shows.

what about time?

and besides, if we didn't have infinity, what would happen to infinite discontinuities? i love those things. :D

What does nature have to do with anything when deciding what is a "valid" mathematical concept?

Don't forget,

an engineer thinks that his equations are an approximation to reality,
a physicist thinks reality is an approximation to his equations,
a mathematician doesn't care.

I think you mean

an engineer puts numbers into his equations because he was told to
a physicist comes up with the equations to approximate reality
a mathematician makes up stuff for the physicists to approximate with

Engineers care a lot about reality. Equations are just another tool.

Mathemeticians care a lot about equations. Reality is an inconvenience :D

Physicists are the wonderful people in between, who care a lot about the boundary - how can we describe reality using equations!

Infinity is useful only for approximations. One thing I dislike about people using infinity is that they treat it like a number, which it is not. It's the nonexistant 'limit' of a neverending process (and is thus limited by time).
There are discrete things in nature. Every discrete thing has a boundry. A boundry is infinitely thin. Welcome to one of the many magical uses for infinity.An infinitely thin boundary is not a real thing.
What does nature have to do with anything when deciding what is a "valid" mathematical concept?Math is supposed to be a tool for use in reality, but sometimes doesn't accurately reflect reality. Reality determines a valid concept. When a concept is valid in the mathematical paradigm, but not in reality, this points to a need for a change in the paradigm.

Math is supposed to be a tool for use in reality, but sometimes doesn't accurately reflect reality. Reality determines a valid concept. When a concept is valid in the mathematical paradigm, but not in reality, this points to a need for a change in the paradigm.

I have to disagree. There are many interesting mathematical results that have no apparent use in reality. This is no reason to toss the work out or abandon that direction- over time someone might find a use for it, if not it's still potentially interesting in it's own right. Look at non-Euclidean geometry, or all the work done on prime numbers two hundred years ago. Who the hell at the time had a real application for estimating the number of primes in a very large interval? Now, these sorts of results make cryptography go round.

A large percent of research mathematicians just do math with little or no regard to reality. Someone else can worry about that later.

What about vacuum? Sure there's a lot of stars and planets but what about the nothingness? There's got to be an infinite amount of that although technically it doesn't exist.

This thread would probably have been better placed in philosophy or something.

Infinity is of course an invaluable mathematical tool.

But Frisbinator is right about infinity not being observed in reality. Many people take it for granted and think of 'the universe' as being infinite when that simply isn't the case. Time also is not infinite from a relativity standpoint. It seems something must be infinite even if it is but infinite recurrance, but that hasn't been observed.

An infinitely thin boundary is not a real thing.Show me a boundary which ISN'T infinitely thin. The line may wiggle and curve... but it's infinitely thin.

No, that doesn't mean it doesn't exist. It just means that you couldn't prove it.



Anselm's theorem: (http://www.utexas.edu/cola/depts/philosophy/faculty/koons/phl349/349lec07.htm)

<i>
1. Something is God if and only if it is something than which no greater can be conceived (abbreviate STWNGCBC).

2. God exists in the understanding, at least. (We can at least conceive of God’s existing in reality).

3. If God existed in the understanding but not also in reality, then we could conceive of a being that is greater than God, namely, a being with all of God’s other perfections plus the additional perfection of actual existence).

4. Therefore, if God did not exist in reality, then we could conceive of a being that is greater than STWNGCBC. (From 3 and 1.)

5. It is logically impossible that we conceive of a being greater than STWNGCBC.

6. Therefore, God must exist in reality.

</i>

Ok lets replace the god with infinity:

1. Something is infinity if and only if it is something than which no greater can be conceived .

2. Infinity exists in the understanding, at least. (We can at least conceive of infinity’s existing in reality).

3. If infinity existed in the understanding but not also in reality, then we could conceive of a number/distance that is greater than infinity, namely, a massure with all of infinity's other qualities plus the additional quality of actual existence).

4. Therefore, if infinity did not exist in reality, then we could conceive of a number/distance that is greater than the point one: Something is infinity if and only if it is something than which no greater can be conceived . (From 3 and 1.)

5. It is logically impossible that we conceive of a number/distance greater than something that cannot be greater.

6. Therefore infinite number/distance must exist in reality.

Show me a boundary which ISN'T infinitely thin. The line may wiggle and curve... but it's infinitely thin.

Here's a hydrogen atom... where does the electron cloud begin?

I have to disagree. There are many interesting mathematical results that have no apparent use in reality. This is no reason to toss the work out or abandon that direction- over time someone might find a use for it, if not it's still potentially interesting in it's own right.I didn't say it should be simply tossed out. That's not how it works normally. And yes, there are instances where mathematical concepts have become useful in reality that previously where considered mere oddities (complex numbers are used in electrical engineering). I could still argue that while being useful, they are only approximations.
Potentially interesting doesn't exactly make it very useful. :P
Infinity is of course an invaluable mathematical tool.

But Frisbinator is right about infinity not being observed in reality. Many people take it for granted and think of 'the universe' as being infinite when that simply isn't the case. Time also is not infinite from a relativity standpoint. It seems something must be infinite even if it is but infinite recurrance, but that hasn't been observed.I agree with this quote.

Show me a boundary which ISN'T infinitely thin. The line may wiggle and curve... but it's infinitely thin.Hrm, this is a tough one... Lets see... Maybe the touchdown line on a football field? Or any number of other boundaries that actually exist... Now show me one that is infinitely thin.

Anselm's theorem:

1. Something is God if and only if it is something than which no greater can be conceived (abbreviate STWNGCBC).

2. God exists in the understanding, at least. (We can at least conceive of God’s existing in reality).

3. If God existed in the understanding but not also in reality, then we could conceive of a being that is greater than God, namely, a being with all of God’s other perfections plus the additional perfection of actual existence).

4. Therefore, if God did not exist in reality, then we could conceive of a being that is greater than STWNGCBC. (From 3 and 1.)

5. It is logically impossible that we conceive of a being greater than STWNGCBC.

6. Therefore, God must exist in reality.This is not a valid argument. The argument presumes the conclusion, among a number of other flaws. The argument actually only gets worse when you replace God with infinity.

Here's a hydrogen atom... where does the electron cloud begin?Basic QM will tell you that there IS a definite boundary... you just can't figure out where that is.

Basic QM will tell you that there IS a definite boundary... you just can't figure out where that is.

Oh... I was under the impression that quantum uncertainty was not simply about limits of detection, but (at least potentially) about actual reality.