Desription and arguement - el Infinite

Let 0*infinity = a for any real (ie finite) a.

The definition properties of 0 include that b*0 = 0 for all real b.

Therefore

b*a = b*0*infinity = 0*infinity = a

So b*a = a, so a=0.

However, consider the quantity \(f(n).g(n)\) where \(f(n) \to 0\) as \(n \to \infty\) and \(g(n) \to \infty\) as \(n \to \infty\). What's \(f(n).g(n)\)? Depends entirely on what f and g are and how you do the limits.

For instance, \(\lim_{m \to \infty} \Big( \lim_{n \to \infty} \big( f(n).g(m) \big) \Big) = 0\) but \(\lim_{n \to \infty} \Big( \lim_{m \to \infty} \big( f(n).g(m) \big) \Big) = \infty\)

But \(\lim_{n \to \infty} \big( f(n).g(n) \big) \) depends on the functions.

If \(f(n) = \frac{1}{n}\) and \(g(n) = kn\) then \(\lim_{n \to \infty} \big( f(n).g(n) \big) = \lim_{n \to \infty} \big( k \big) = k\)
If \(f(n) = \frac{1}{n^{2}}\) and \(g(n) = kn\) then \(\lim_{n \to \infty} \big( f(n).g(n) \big) = \lim_{n \to \infty} \big( \frac{k}{n} \big) = 0\)
If \(f(n) = \frac{1}{n}\) and \(g(n) = kn^{2}\) then \(\lim_{n \to \infty} \big( f(n).g(n) \big) = \lim_{n \to \infty} \big( kn \big) = \infty\)

So you cannot define it in any consistent way.

 

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Something and nothing.

 

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Quantum Heraclitus:

The second moment is the realization of the possibility in the first. As such, it turns red. The change is "blink, red!". In reality, change is far more gradual for almost anything.

Another way to view it:

Time 1: 01
Time 2: 10

 

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why is it so important to understand the nature of nothing?
do you think your focus is improved by focusing on nothing?
If in in understanding nothing we lose our understanding of everything else, then what is the cost of knowing nothing?

 

We do not lose our understanding of everything else. As such, we're fine.

But yes, it is useful on a practical sense for keening the mind.

 

say we have a particle travelling close to 'c' and it moves a total of 1 foot from segment blue [position B] to segment red [position R]

How did it get to position R from position B
Did it just blink and appear AT position R?
What happened in the distance in between?

 

One cannot put a number on the difference (and this is a property of it by definition.) It's not quite a 0 difference, but it's as close as possible. Mathematicaly, the infinitesmal can be expressed as lim x as x approaches 0, and thus, lim x-0 as x approaches 0 is 0, and hence, the mathematical difference is 0 (at least in this function.)

Aye that's pretty much it.

I could make a few arguments for it, but I don't have any sources on hand; and a google search yielded no trustworthy sources (though I should point out that the general message board concensuss does affirm your position; though these matters of calculus seem to be akin to those of QM; just within the vocabulary of many, and just out of the knowlege.) Anyway; I'l hunt around for a good source, and see what it has to say.

However, AlphaNeumeric has provided a few functions in which demonstrate the fallacy in defining 0*infinity. That should be sufficient I hope.

Consder this: f(x)= x! (x factorial)
It's domain is in the positive integers (inclusive of 0).
Clearly, in the smallest possible change in x, there is a change in f(x). But f(x) always evaluates to the same value given a constant x. Thus, consider f(1) and f(2), both individual points are true point (and fit your use of 'static') both are side by side, and directly beside each other in this functions domain: there can be no smaller value between them. So how does the function change?

Hell if I'm going to answer that; seems more philosophical to me, but we can easily see that it does, and that is all that matters.

By definition, there is nothing in between. Indeed, what happened between 1 and 2 of the above function?

Integers not doing it for you? Lets head into the reals: even in the function f(x)=x, each value is in 'stasis:' the points are truly discrete and 0-dimensional.
Yet, a change definatly happens between the points on the functions, proving that a change should just as well happen in time. Even if we use a limit to pick to find the difference between the smallest two possible points on a function; we still measure a rate of change (this is where the derivative comes from.) even if the change between those two points is incomprehensably small.


Alright, that's eanough limits for one day >.>
-Andrew

 

My question may be inappropriate due to misunderstanding but,
even if we simply declare that 1 becomes 2 in math do you feel this is suffient in describing how 1 becomes 2 in physics.
To me it is far from sufficient to simply say that 1 becomes 2 and thats that.

How would blue become red when there is no time to provide for the transition?
For an object to go from point A to point B it does actually have to move, one would think unless we are declaring that somehow miraculously movement occures when there is no time to do it in.

Just because this an accepted mathematical process does not make it IMO a physical one.
Is my question inapporpriate and mistaken?

 

Anbna,
Can I ask if you hold to PJs notion that the light cones are separated by an infinitisemal time segment. In that the point between past and future has infinitesimal moment called the NOW or Present?
All indications suggest that this point between past and future is in fact zero duration and thus zero stasis according to the lightcone diagrams.

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Possibly you would like to speculate on what would happen if the separation between past and future had a moment of stasis [ infinitesimal small duration] and how that would effect the spacetime theory as put forward by Albert E. and his mates.

 

Quantum Heraclitus:

It could not move 1 foot in an infinitesimal time span. Only something which is travelling at infinite speed could move more than something far less than a planck length of space.

 

Andbna:

I think the later thing we spoke about covered this, then.

But man, Zeno's paradoxes really work, with a bit of tuning from time to time, for so many things. That Eleatic bastard!

I'm going to see if I can contact a professor of mathematics and see whether he can give me a decent, quick answer to the question of why 0 * oo = ?. I think that is one of the most reliable ways to go about those sort of things. I know I have no book on hand that ought to explain that. I only have a math text book or two and Euclid's "Elements" on hand.

Again, thank you for the excellent explanation.

Andy you're a star in nobody's eyessss but mineee.

Yes, I am serenading you with pop music.

 

given that you know what my question is and of course the figures quoted are examples only and not actual you have still avoided answering the question!
How does one segment make the transition to the other in physics and not math?

how does blue become red with out transition?

 

Andbna has graceously shown why this is possible in mathematics but as yet failed to show how this is possible in physics.

Understandably math requires finite points along a line, but these are mathematical imagery and not necessarilly physics or should I say of material value.
Am I wrong or am I right?

 

Quantum Heraclitus:

How am I supposed to know the answer to this question? We're talking about coloured lines. What physics can be answered with things which are not objects of physics?

But I'll try an analogy to a transistor, in line with my previous pseudo-binary answer.

A transistor has two settings: On and off.

Let red represent on, let blue represent off.

Let the switch be able to take one infinitesimal moment (that is the next moment).

If red, it will be blue in the next moment. If blue, it will be red in the next moment.

 

From what I understand, all we are doing is demonstrating the limitations of mathematics when attempting to apply it to the real world.

 

Quantum Heraclitus:

One thing ought to be stressed: The majority (in fact everything) in physics can be translated into mathematical language. Of course, the mathematics doesn't prove the physics, but the physics is certainly speakable in terms of mathematics. The inverse square law, E=MC2, all that nonsense.

Logically it does follow that material substance should be infinitely reducible if it can be finitely reducible, which it is clear it can be.

I can go a mile to the mall, or half a mile to the grocery store, or a quarter of mile to the laundry, an eighth of a mile to the bodaga, a sixteenth of a mile to my neighbour's, a 32nd of a mile to my garbage can, 1/64th of a mile to my living room...

 

hmmmm...

The transistors current flow must fall quickly but not instantaneously to zero as the flow diminishes to zero,
Can a a current flow go from say 1 amp to zero instantaneously.

I do not think so....

A bit like trying to stop a river from flowing by shutting a gate in a damn. It will always take time no matter how fast you are to go from flow to no flow.

 

I have a funny name for a principle:

The Gandalf Principle.

Or "You will not pass!"

"Barring demonstration of the contrary, a finite process can be extended infinitely."

 

However there is a limit to how mathematics can explain reality as described in the use of infinity. Regarding the 12" brick. Infinitey from what I understand can only make sense if limited in mathematics. If left unlimited it looses it's value of utility. All you are showing is this limitation IMO and not the reality.
Besides the distances you speak of are arbitary and have nothing to do with physical reality but more to do with epistemoligical conveniance.

 

Quantum Heraclitus:

Ideally, yes. If we're talking about timescales and spatial sizes on the infinitesimal.