[PmbPhy]

Yes my flawed logic. Apologies Pete.

No problem my dear Jeff. What I admire about you is your astute ability to both recognize your mistakes and admit them. Something a lot of people don't have the ability to do.

[Bill S]

n+∞=∞

That’s OK as long as you are talking about mathematical infinities.  If you are talking about an infinite cosmos, then n+∞=∞ has no real meaning, because the infinite cosmos is all that exists, or can exist; in which case there is no 1 to add to infinity.

[Bill S]

Not at all. The definition of any infinity is absolutely precise. Take the simplest infinity: 1/x where x→0. x=0 is an absolutely precise statement, not an approximation to anything.

This is probably a very naïve question, but is x→0 the same as x→ ∞?

[jeffreyH (OP)]

Yes my flawed logic. Apologies Pete.

No problem my dear Jeff. What I admire about you is your astute ability to both recognize your mistakes and admit them. Something a lot of people don't have the ability to do.

Reasoned debate is more productive than unreasoned bile. I would rather learn from mistakes than keep repeating them. I often spout nonsense but it takes me a while to realize it.

[Bill S]

n-∞=-∞

I've been trying to get my head round that one.  How do you define minus infinity?  It's a fascinating thought, but it beats me.   []

Alright, already! I know that's easy when it comes to maths.

[JohnDuffield]

That’s OK as long as you are talking about mathematical infinities.  If you are talking about an infinite cosmos, then n+∞=∞ has no real meaning, because the infinite cosmos is all that exists, or can exist; in which case there is no 1 to add to infinity.

We just don't know that the universe is infinite, Bill. I don't think it can be, because the universe has a finite age, I do not accept that it was already infinite when the big bang occurred, and I don't see how an infinite universe can possibly expand because the "pressure" is counterbalanced at all locations.

This is probably a very naïve question, but is x→0 the same as x→ ∞?

No. We have plenty of instances where something diminishes to zero, but we have no evidence that there are any infinities in nature. When they crop up, such as with a black-hole point-singularity, they are thought to signify some breakdown in the mathematics and in our understanding.

[alancalverd]

I have no problem with the number of cats you may have on your roof, nor would I dispute the intricacies of set theory.  What I have to ask is: Are you saying that Jeffrey was wrong when he said that “any system that can normally be considered as bounded cannot include an infinite component.”? 

Yes, he was wrong. Hence my example that there is an infinity of rational numbers in any interval. The interval between 0 and 1 contains 1/2, 1/3, 1/4....2/3, 2/4, 2/5,....3/4, 3/5, 3/6....and so on - i.e. an infinite number of rationals exist between the bounds of 0/1 and 1/1. Whilst the number of rationals in an interval is not a component of that interval, there is an infinite number of components, so the set of components is infinite and thus the bounded interval contains an infinite component.

[evan_au]

is x→(Finite number) the same as x→∞?

It's not the same, but the two are often related.
For example, relativity has many expressions like 1/√(1-v²/c²)

As v→c, 1/√(1-v²/c²) →∞.

This relationship has been validated to many decimal places in successively higher energies of particle accelerators.

JohnDuffield points to another example in a black-hole point-singularity, but in that case it is likely that the quantum nature of space and particle tunneling will provide a lower limit on the degree to which the inverse square law applies as distance x→0 (but we currently have no tested theory of quantum gravity).

[jeffreyH (OP)]

I have no problem with the number of cats you may have on your roof, nor would I dispute the intricacies of set theory.  What I have to ask is: Are you saying that Jeffrey was wrong when he said that “any system that can normally be considered as bounded cannot include an infinite component.”? 

Yes, he was wrong. Hence my example that there is an infinity of rational numbers in any interval. The interval between 0 and 1 contains 1/2, 1/3, 1/4....2/3, 2/4, 2/5,....3/4, 3/5, 3/6....and so on - i.e. an infinite number of rationals exist between the bounds of 0/1 and 1/1. Whilst the number of rationals in an interval is not a component of that interval, there is an infinite number of components, so the set of components is infinite and thus the bounded interval contains an infinite component.

Physically you cannot go on sub-dividing space. You hit the Planck scale before you know it. As far as maths goes you are right but you soon run into a Zeno's paradox at very small physical scales.

[PmbPhy]

JohnDuffield is a major crackpot - Beware!!!!

[Bill S]

JohnDuffield is a major crackpot - Beware!!!!

The geological cognoscenti said that about Alfred Wegener. 

Many still say it about Warren Carey, but he is still a geologist of considerable stature.

[Bill S]

In another thread; in response to my saying that there could never have been nothing, otherwise there would still be nothing now; JP pointed out that we could not make this claim because, outside the Universe conditions could exist in which something could come from nothing. He assured me that to substantiate my claim scientifically I would have to provide proof that such conditions could not exist.

Let’s apply this to the infinity argument.

……an infinite number of rationals exist between the bounds of 0/1 and 1/1.

Is this a scientifically valid claim? 

How could anyone prove that there was not something that would prevent this from being a physical reality?  Smallest possible divisions, quanta etc? 

Can anyone identify an “infinite” point?   Of course not; in fact that is a ridiculous question.

If a physical infinity exists, it cannot exist within a finite universe – in fact the finite universe would have to exist within the infinite entity.

[Bill S]

For example, relativity has many expressions like 1/√(1-v2/c2)

As v→c, 1/√(1-v2/c2) →∞.

Does 1/√(1-v2/c2) go to infinity, or to 0?

[jeffreyH (OP)]

For example, relativity has many expressions like 1/√(1-v2/c2)

As v→c, 1/√(1-v2/c2) →∞.

Does 1/√(1-v2/c2) go to infinity, or to 0?

When v^2 = c^2 the square root operates on zero. Within the currently known laws of physics V cannot exceed c so zero would be the limit when velocity is increasing. However we then end up with 1/0 which is undefined. I disagree with this equaling infinity. When v tends to zero the square root then is √(1-0/c^2). Then we have 1-0 and with the square root of 1 being 1 the whole expression is 1/1. So in this situation the limit is 1. We can equate this to multiplying by one which gives us 100% of an original value. This means that as the value tends towards undefined we end up with a decreasing amount of the original value until the mathematics eventually breaks down at undefined.

[jeffreyH (OP)]

Let us take a simple equation A*B = C. It follows that A = C/B. What if we set B to zero. A*B = C then becomes A*0 = 0. Now if A > 0 what is the meaning of A = C/B if C is also > 0? In this case and to make sense C has to tend towards zero and equal B when exactly zero. This is why were are missing a component in the relativistic equations. This does not mean that C and B are always equal but they must be equivalent when they reach zero. They must both cross the origin.

[Bill S]

Jeff (is it OK to call you Jeff), I usually have to substitute numbers for letters to make sure I have grasped algebraic equations. 

In this case I get:

A*B=C     A=C/B     If A=2 & B=0

2x0=0        2=0/0 which makes no sense to me.

After that you lose me.  How do you get from C=0 to C tends towards 0

[JohnDuffield]

...Let’s apply this to the infinity argument.

……an infinite number of rationals exist between the bounds of 0/1 and 1/1.

Is this a scientifically valid claim?

No. Take a look at your ruler. There isn't an infinite number or amount of anything between the 0 and the 1. People who talk about dividing up that distance into some infinite subdivision are getting lost in abstraction. 

How could anyone prove that there was not something that would prevent this from being a physical reality?  Smallest possible divisions, quanta etc?

You can't disprove this sort of thing, just as you can't disprove fairies. 

Can anyone identify an “infinite” point? Of course not; in fact that is a ridiculous question.

It all gets very abstract and very ridiculous very quickly. But when you point this out, some guy who can't point to any supporting scientific evidence starts calling you names.

If a physical infinity exists, it cannot exist within a finite universe – in fact the finite universe would have to exist within the infinite entity.

I agree. There ain't no infinities in nature. None that we know about. And I don't see that changing any time soon.

...However we then end up with 1/0 which is undefined. I disagree with this equalling infinity...

Well said Jeffrey. We talk about infinite time dilation for the hypothetical guy travelling at c, but what it really is, is zero local motion.   

[jeffreyH (OP)]

Jeff (is it OK to call you Jeff), I usually have to substitute numbers for letters to make sure I have grasped algebraic equations. 

In this case I get:

A*B=C     A=C/B     If A=2 & B=0

2x0=0        2=0/0 which makes no sense to me.

After that you lose me.  How do you get from C=0 to C tends towards 0

Sorry Bill that was rushed. You are right that when A = 2 then both C and B cannot both be zero. I set A to 2 to show that the only way round the division by zero was for C also to equal zero which then invalidates A. Anyway that was the point I was trying to make. In my view setting a denominator to zero means your value ceases to exist. Whatever the value be it radius, mass or anything else. In calculus this can be used as a limit in determining a derivative but to think of it actually representing a physical value is not at all useful.

[PmbPhy]

I agree. There ain't no infinities in nature. None that we know about. And I don't see that changing any time soon.

Yet another ignorant comment again. The self energy of any point charged particle is infinite. See http://quantummechanics.ucsd.edu/ph130a/130_notes/node44.html

The mass/energy density of the universe is uniform so since a certain percentage of that matter consists of hadrons it follows that there are an infinite number of hadrons. All of these are infinite and known to all physicists who know what they're talking about.

[jeffreyH (OP)]

I agree. There ain't no infinities in nature. None that we know about. And I don't see that changing any time soon.

Yet another ignorant comment again. The self energy of any point charged particle is infinite. See http://quantummechanics.ucsd.edu/ph130a/130_notes/node44.html

The mass/energy density of the universe is uniform so since a certain percentage of that matter consists of hadrons it follows that there are an infinite number of hadrons. All of these are infinite and known to all physicists who know what they're talking about.

What does the self energy correction say about the state of the field energy in the immediate vicinity of the electron?