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[G-Flex]

Um... 0*∞ is 0. That's why photons actually can travel at the speed of light, because they have no mass.

Zero times infinity seems to be an undefined quantity. When evaluating limits (which is where infinity comes into play anyhow), it's an indeterminate form.

[Neruz]

He said he tested with an underground pool, so that's horizontal; he probably channeled out water from the top level and thus his system has only the rest pressure of the even level, which is why it's not flowing up to the next level, as water at rest pressure (unpressurised basically) only ever flows to z-1, for some strange unknown reason.

Um... 0*∞ is 0. That's why photons actually can travel at the speed of light, because they have no mass.

Zero times infinity seems to be an undefined quantity. When evaluating limits (which is where infinity comes into play anyhow), it's an indeterminate form.

Zero times infinity is meaningless and illogical, as infinity is not a number.

[smjjames]

So...... we'll be seeing some strange water behavior in the next release, you think?

That sounds like what Shoku is getting at.

[Neruz]

Unless Toady has redone the pressure system, which i doubt, as it's not mentioned anywhere, we'll be seeing exactly the same water behavior. It's a bit odd when unpressurised, but otherwise isn't that perculiar when you know what rules it operates on.

[smjjames]

I doubt he would have messed with the pressure system without letting us know.

[shadow_slicer]

Spoiler: more physics (click to show/hide)

If you going fast enough, it will seem to you that you traveled faster than light.

Why would it seem that way?? Relative speed is always symmetrical. If you travel almost at c from an outside observer, the outside observer will travel with almost c from your viewpoint...

That's not necessarily true. Why does relative speed have to be symmetrical? The fact is that if you are traveling near the speed of light your seconds become much longer than a stationary observer. Your meters become much longer than a stationary observer's. Because the basic units you measure speed in are different, there is no reason you must calculate the same value for your speed. This means you would calculate your speed to be faster than the speed of light, while a stationary observer would measure your velocity to be below the speed of light.

(Photons don't seem to have infinite mass, because they have no rest mass.  Zero times infinity gives you the mass of the photon, which is why photons can have differing masses.)

Uhm what?

Photons have a mass dependent on their frequency. DreamThorn  is probably trying to explain the seeming contradiction: 1) As objects accelerate to the speed of light their mass increases multiplicatively towards infinity 2) photons move at the speed of light, but have finite mass. This is explained by setting the rest mass of the photon to "0". Well not really 0 per se, but instead an appropriate limit that is effectively 0 at rest, but cancels the infinity at the speed of light to give the correct value of mass for the photon.

[zchris13]

It doesn't make sense it doesn't have to.  Our best theories are only approximations.  The universe is MAGIC.

[Neruz]

Spoiler (click to show/hide)

(Photons don't seem to have infinite mass, because they have no rest mass.  Zero times infinity gives you the mass of the photon, which is why photons can have differing masses.)

Uhm what?

Photons have a mass dependent on their frequency. DreamThorn  is probably trying to explain the seeming contradiction: 1) As objects accelerate to the speed of light their mass increases multiplicatively towards infinity 2) photons move at the speed of light, but have finite mass. This is explained by setting the rest mass of the photon to "0". Well not really 0 per se, but instead an appropriate limit that is effectively 0 at rest, but cancels the infinity at the speed of light to give the correct value of mass for the photon.

Spoiler (click to show/hide)

The word you're looking for is 'infinitesimal', a concept that is infinitely close to zero, but is not zero, and when 'multiplied' (technically impossible, but it works as a description) by infinity you get a finite result depending on the size of the infinity and infinitesimal in question.

[PermanentInk]

Zero times infinity is meaningless and illogical, as infinity is not a number.

Limit of 0*n as n approaches infinity, then?  Seems like a workable formulation to me.

[Neruz]

Zero times infinity is meaningless and illogical, as infinity is not a number.

Limit of 0*n as n approaches infinity, then?  Seems like a workable formulation to me.

What i meant was that 'infinity' is not a number. It is the concept of something without end, in your example, n is a number without end, it is infinite, but it is not in itself infinity.

Nitpicking at the language a bit, but it is extremely important when dealing with infinite functions to ensure you're using the right words, as otherwise it very rapidly becomes impossible to work out what the hell anyone is talking about.

[zchris13]

Math can be so illogical.

[Christes]

It's plenty precise, but humans are illogical.

Spoilered for those who don't care about math talk:

Spoiler (click to show/hide)

Infinity is not a real number.  As such, it's not clear what 0*∞ should even be

If you want, it's totally legal to adjoin ∞ to the real numbers if we want to and define 0*∞ = 0.  But then it wouldn't be the system of real numbers, and I could just as well define 0*∞ = 1 or 0*∞ = 32. But regardless of what I set it to equal, it won't behave nicely or follow the properties we typically want out of numbers.  This is why we usually don't include it.

It is also completely possible to make an arithmetic out of the different cardinalities of infinity, so that you can add, multiply, and exponentiate infinites and stuff, but that can get a little complicated for this forum, I think.

[Neruz]

It's plenty precise, but humans are illogical.

Spoilered for those who don't care about math talk:

Spoiler (click to show/hide)

Infinity is not a real number.  As such, it's not clear what 0*∞ should even be

If you want, it's totally legal to adjoin ∞ to the real numbers if we want to and define 0*∞ = 0.  But then it wouldn't be the system of real numbers, and I could just as well define 0*∞ = 1 or 0*∞ = 32. But regardless of what I set it to equal, it won't behave nicely or follow the properties we typically want out of numbers.  This is why we usually don't include it.

It is also completely possible to make an arithmetic out of the different cardinalities of infinity, so that you can add, multiply, and exponentiate infinites and stuff, but that can get a little complicated for this forum, I think.

Precisely; Infinity is a concept, not a number.

[dragnar]

but that can get a little complicated for this forum, I think.

Really? A forum where discussions of quantum physics come up from discussions of throwing mechanics can't handle tough math? This forum has some of the most complex discussions I have ever seen on the internet.

[Christes]

If by "number" you mean "Real number," then absolutely.  But I really feel the need to nitpick your language now too   Spoilered for the eyes of decent human beings:

Spoiler (click to show/hide)

3 is simply a symbol, as is 0 and 6 and 4.2 and ∞ and so many more.  They all represent concepts in a sense.  When we say something like 1+1=2 we have a string of symbols.  We have a system that defines this string to be true, and others to be false.  But that's just the system we're used to. 

Like I said, you can create a system where the "numbers" are the sizes of sets, both finite and infinite.  There are mathematically well-defined ways to talk about addition and multiplication of these and so on.  In a way, this makes infinity a "number," just not in the number system we are used to working with.  If you are limiting yourself to the traditional mathematical land of reals and complex numbers (which I assume you are doing), then you're perfectly cool in saying that infinity is not a number.  And when someone asks what ∞*0 equals they are indeed usually missing the point.

It's just that, formally speaking, there really isn't a good definition of what a "number" even is.

Really? A forum where discussions of quantum physics come up from discussions of throwing mechanics can't handle tough math? This forum has some of the most complex discussions I have ever seen on the internet.

I mean complicated to type the symbols I need.  And, really, I get annoyed when advanced topics spring up in public areas anyway.