Are we too free with infinity?

[mistermack]

After a discussion on another thread, I'm offering the opinion that we are far too happy to throw in the term infinity, when we really shouldn't.
I've thought back to times when I've said 'there are an infinite number of this, or that', and realised that in every case, it's been wrong.

In the example that made me think about it, a member said, '' there are an infinite number of real numbers between 1 and 2 ''. Which was confirmed by two other members, so I'm assuming it's an official position in the maths textbooks.

I felt that this would produce nonsensical results, without giving it much attention.

But if you think about it, SHOULD we use infinity in that way?
In every situation that comes to mind, the words '' there are '' are actually incompatible with the word infinity, even in maths.

Take the described example. When you say ''there are an infinite number'', you are actually saying that there is such a thing as an infinite number. But infinity can never be a number, it can never be attained, it goes on increasing ad infinitum. So I thought, what should we say instead?
There are an infinite number of possible numbers between 1 and 2? It sounds ok, but actually the problem remains the same. When you say '' there are'', you're still stating that it's POSSIBLE that infinity can be reached. Perhaps if you said 'theoretically', that would cover it? I don't think it helps. You are throwing in a incorrect theory.

So perhaps you could say '' there is a mechanism that will produce real numbers between 1 and 2, which would produce numbers ad infinitum''.
I think that is still wrong, because ad infinitum means an infinity of time, and that is just as unattainable.

To me, the words '' there is '' or '' there are '' seem to be incompatible with the word infinity, or ad infinitum, or any other variant, when you really examine it.
The very words contradict each other. I think we should never say that there is an infinite anything.
( at least, I can't think of anything ).

I recently wrote that there are an infinite number of directions a particle can travel. But is that really the case? I blythely assumed it, with no justification at all. All we know is that the number of possibilities is very very large. But that is TOTALLY different to infinite.
when I said there was an infinite number, that was wrong, and also, it makes assumptions of the nature of spacetime at the infinitessimaly small scale that are not supported by any evidence at all.

So I'm looking for valid examples, either physical or mathematical, where you can legitimately say ''there is infinite''.
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[Farsight]

I don't think there are any, mistermack. As far as I know, there are no infinities in nature. Infinity is just a concept. It's a useful concept I suppose, but sometimes people take it too literally.

I quite like the word "unbounded" as a sometimes-apt alternative.

[Feck]

Tends towards infinity ? as infinity cannot be reached or measured things tend towards it .

[PsychoSerenity]

I don't even ...






Oh well,

[FBM]

Like square root of -1. Also a convenient, useful fiction. We can do a lot by pretending that it refers to something, but at the end of the day, we have to admit that it doesn't.

[ChildInAZoo]

Almost every use of infinity in science has a constructive use. That means that we can speak of it only in terms of mathematical results that we can demonstrate.

So for the case of real numbers, we always have a procedure for producing a third real number between any other real number. For prime numbers, we always have a means of producing a larger prime number. For directions, we always have a means of identifying a direction that is not identical to any previously given direction.

Similarly, when one speaks of finite in a constructive way, then we speak of something for which we have a demonstrable way of exhaustively listing.

[colubridae]

Like square root of -1. Also a convenient, useful fiction. We can do a lot by pretending that it refers to something, but at the end of the day, we have to admit that it doesn't.

I always hated the use of the square root of -1 and calling numbers such as i5 'imaginary'.

Putting i in front of a real number simply means "change the way you operate the rules on this number. "
such that
If you multiply it with another 'imaginary' number and both are negative the result is negative not positive (and becomes real) as with a 'real' number.

Sadly i and imaginary are entrenched in usage.


edit spelling

[mistermack]

Tends towards infinity ? as infinity cannot be reached or measured things tend towards it .

Actually, yes, I suppose that's what ad infinitum means. In common usage, we usually take it to mean ''for ever'' instead of ''towards forever''.
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[mistermack]

So for the case of real numbers, we always have a procedure for producing a third real number between any other real number. For prime numbers, we always have a means of producing a larger prime number. For directions, we always have a means of identifying a direction that is not identical to any previously given direction.

That illustrates what I'm saying really. What we have is a procedure, or a means. What we don't have is an infinite number of anything.
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[ChildInAZoo]

That illustrates what I'm saying really. What we have is a procedure, or a means. What we don't have is an infinite number of anything.
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Just because we have such a procedure does not mean that there is not an infinite amount of anything. What it does mean is that anyone who claims that physics is incorrect because it refers to infinity must actually pony up a specific example.

[mistermack]

Just because we have such a procedure does not mean that there is not an infinite amount of anything. What it does mean is that anyone who claims that physics is incorrect because it refers to infinity must actually pony up a specific example.

Now there's a couple of nice strawmen. I didn't say that because we have such a procedure, there is not an infinite amount of anything. I said that to say that we have an infinite amount of anything is illogical. Infinity is not an amount. It could never be an amount. So there can never be an 'infinite amount'.

And I didn't claim that ''physics'' is incorrect either (whatever that means). I don't claim it's incorrect to REFER to infinity. I am offering the opinion that it's not valid to say that there IS an infinite amount of anything, whether it be numbers, angles or particles or waves.
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[ChildInAZoo]

Now there's a couple of nice strawmen. I didn't say that because we have such a procedure, there is not an infinite amount of anything. I said that to say that we have an infinite amount of anything is illogical. Infinity is not an amount. It could never be an amount. So there can never be an 'infinite amount'.

But it is not illogical to speak of sets with infinite cardinality. And physics does allow that there are infinite spatial distances and that the set of all particles has infinite cardinality. The standard cosmological model is, as yet, agnostic about whether or not the universe is infinite in spatial extent or not. To claim that it is illogical to speak of an infinite amount is to say that certain theories of physics are wrong.

[colubridae]

Just because we have such a procedure does not mean that there is not an infinite amount of anything. What it does mean is that anyone who claims that physics is incorrect because it refers to infinity must actually pony up a specific example.

Now there's a couple of nice strawmen. I didn't say that because we have such a procedure, there is not an infinite amount of anything. I said that to say that we have an infinite amount of anything is illogical. Infinity is not an amount. It could never be an amount. So there can never be an 'infinite amount'.

And I didn't claim that ''physics'' is incorrect either (whatever that means). I don't claim it's incorrect to REFER to infinity. I am offering the opinion that it's not valid to say that there IS an infinite amount of anything, whether it be numbers, angles or particles or waves.
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Look I'm not trying to be argumentative or nasty, I admit in the past that I''ve deliberately laughed at you for saying stupid things.

But really, nothing anyone says here has been of any use to you at all. Others (ok, not me) have been very patient and tried to explain things to you but you've shown no real interest in what they say. All you want to do is ignore what they say and argue.

I'm new here as well, but what they say seems to be what I think, so I'm happy and I stay.

But nothing anyone says seems ok by you, you seem only to want to tell them they are wrong.

Are you sure this is the right place for you?

[ChildInAZoo]

All you want to do is ignore what they say and argue.

"Argument is an intellectual process. Contradiction is just the automatic gainsaying of any statement the other person makes."

[mistermack]

There's an infinite amount of nothing? I have to agree that's possible. But meaningless.
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