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JohnDuffield is a major crackpot - Beware!!!!

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

For example, relativity has many expressions like 1/√(1-v2/c2)As v→c, 1/√(1-v2/c2) →∞.

Quote from: evanFor 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?

...Let’s apply this to the infinity argument.Quote from: alancalverd ……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.

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

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=02x0=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

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

Quote from: JohnDuffieldI 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 ...sorry, you cannot view external links. To see them, please REGISTER or LOGINThe 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.

Even in classical electromagnetism, if one can calculates the energy needed to assemble an electron, the result is infinite, yet electrons exist. The quantum self energy correction is also infinite although it can be rendered finite if we accept the fact that out theories are not valid up to infinite energies.

Quote from: alancalverd ……an infinite number of rationals exist between the bounds of 0/1 and 1/1.Is this a scientifically valid claim?

For any a there exists at least one number a+1 > a so for any a I can define an appropriate b > a and hence numbers each side of a/b. There being an infinity of a there must thus be an infinity of a/b.

Your statement is a mathematical “truth” which neither requires nor needs physical truth to complete it.

Yet another ignorant comment again. The self energy of any point charged particle is infinite. See ...sorry, you cannot view external links. To see them, please REGISTER or LOGIN

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.

Exactly so. The fact that you would run out of patience long before you ran out of possible subdivisions of the set of rational numbers between 0 and 1 does not however negate the assertion that the set is itself (a) infinite (b) larger than the set of integers and (c) not a continuum.

“I done me best when I was let. Thinking always if I go all goes. A hundred cares, a tithe of troubles and is there one who understands me?"Then there's the Three quarks for Muster Mark!And we're back to physics.

You are a cut above the rest Bill.

Quote from: Jeff You are a cut above the rest Bill. I could be a crackpot, though, couldn't I? []

I think we all have that potential. []

It takes a particular personality for that.

An boundless universe with uniform mass density has an infinite number of galaxies, particles, stars and planets in it and thus an infinite amount of matter.

the set of rational numbers between 0 and 1 ...is (a) infinite (b) larger than the set of integers

∞2=∞.

Yor_on. Your last post seemed to say something interesting; I just wish I knew what it was. []

Well then find the radius of the circle whose circumference is infinite.

The point here is that any system that can normally be considered as bounded cannot include an infinite component. So if the mathematics of a formerly finite system go infinite something is terribly wrong.

Let me make this very clear first; {infinity} is not a number.

There is an infinite number of integers 1,2,3,.... because we can always add one moreThere are rational numbers between the integers 1, 3/2, 7/4, 2, 9/4, 19/8, 3.... Indeed there is an infinite number of rational numbers between any two integersSo the number of rational numbers must be greater than the number of integers

IMHO if ever you bump into an infinity in physics, then something is wrong somewhere.

Nonsense. It's beginning to become clear that the universe is flat and boundless and as such goes on forever, never ending. That's what it means to be infinite.

Infinite answers are certainly not right, so they are a sign that your theory is not very good. A theory needs to fit the data, but it also needs to make mathematical sense.

…… there can never be an infinite amount of distance between any two particles as that would place a boundary on infinity.

If the universe was flat then Sean Carroll would not disagree with me.

Does the fact that we cannot experimentally verify something make it untrue through?

Quote from: PeteIf the universe was flat then Sean Carroll would not disagree with me.OK; but could you explain why, please.

Quote from: Bill SQuote from: PeteIf the universe was flat then Sean Carroll would not disagree with me.OK; but could you explain why, please.Absolutely. If the universe was flat and the cosmological principle (...sorry, you cannot view external links. To see them, please REGISTER or LOGIN) is correct (both of which are widely beginning to be accepted as true) then the universe unbounded and not finite, i.e. the space is not bounded and goes on forever which means that the number of hadrons and hence the amount of matter is infinite. I can't imagine Sean disagreeing with me.

Surely infinity is an unbounded continuity whereas hadrons are discontinuous having gaps of varying magnitude between them. For hadrons to be infinite ...

it would require there being only 1 hadron of infinite size.

For multiple hadrons there would also have to be an infinity of empty space.

If infinity is all inclusive ..

Precise measurements lead cosmologists to conclude that the universe is flat, and thus has infinite volume.

This is very simple, Jeff. Mass density = constant. Volume of universe = infinite

Pete, what you say is undoubtedly right, but, as has already been mentioned, mathematical reality and physical reality are not necessarily the same thing.

E.g. with the “book stacking problem” it is possible, in theory, to reach an infinite overhang ..

with an infinite number of books, but would you claim that is physically possible?

What do you mean by an infinite over hang? Do you mean that the center of mass of the next book to be put on the stack is not right above the previous one and thus there is an increasing over hang? If so then that's not possible because it'd collapse before that.

If that volume increases without limit it means that the mass increases without limit. That's what it means to be infinite.

I am neither qualified, nor would I wish, to suggest that this is not a mathematical reality. However, if you are talking of something "increasing", that something is not infinite. If it is not infinite it is finite and therefore it can never become infinite.

To suggest that this particular example could be applied to every problem in physics would be absurd, and is certainly not something I said.