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[dragnar]

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

Ah, hadn't thought of that.

[CobaltKobold]

Spoiler (click to show/hide)

Integration of Dirac delta function.

[Neruz]

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.

Right, i just wanted to make sure you didn't fall into the usual trap people seem to fall into when they start trying to wrap their minds around infinity.

[Osmosis Jones]

Spoiler (click to show/hide)

Integration of Dirac delta function.

Isn't that 1? Or am I thinking of the Kronecker delta?

[smjjames]

Or maybe its the Amazon Delta?

Yes I have no idea what you are talking about.

[dwr]

Dirac Delta function is, IIRC, 1 for a line integral, Pi for a 2d integral, 4Pi for a 3d integral.

[Sean Mirrsen]

Spoiler (click to show/hide)

I don't wrap my mind around infinity, I just kinda let it wrap itself over me instead. If you imagine infinity (+infinity, specifically) as the endpoint of a hypothetical infinite real vector, it makes sense to have 0 times infinity to make 0, since multiplication by a zero vector will invariably produce a zero vector. In a way, a zero is "more powerful" than infinity, the two are not opposed as the unstoppable spear/unbreakable shield are. In regards to photons and lightspeed, I have two opinions. First, why would anyone assume that the speed of a photon is the actual maximum relativistic speed? It's the fastest thing we know, but if it's a particle (part-particle) with infinitessimal mass, then it moves at a speed that is below the relativity threshold - just enough to make the multiplication "horrendously large" instead of "infinite". Second, and this has no relation to this discussion, I don't think a photon actually exists as a particle, it simply shows particle-like behavior. Not being a particle allows it to trump known laws regarding mass and lightspeed, the particle-like effect is simply moving along with whatever underlying system that causes it to manifest.

[Neruz]

Spoiler (click to show/hide)

I don't wrap my mind around infinity, I just kinda let it wrap itself over me instead. If you imagine infinity (+infinity, specifically) as the endpoint of a hypothetical infinite real vector, it makes sense to have 0 times infinity to make 0, since multiplication by a zero vector will invariably produce a zero vector. In a way, a zero is "more powerful" than infinity, the two are not opposed as the unstoppable spear/unbreakable shield are. In regards to photons and lightspeed, I have two opinions. First, why would anyone assume that the speed of a photon is the actual maximum relativistic speed? It's the fastest thing we know, but if it's a particle (part-particle) with infinitessimal mass, then it moves at a speed that is below the relativity threshold - just enough to make the multiplication "horrendously large" instead of "infinite". Second, and this has no relation to this discussion, I don't think a photon actually exists as a particle, it simply shows particle-like behavior. Not being a particle allows it to trump known laws regarding mass and lightspeed, the particle-like effect is simply moving along with whatever underlying system that causes it to manifest.

Spoiler (click to show/hide)

Because Photons are assholes and refuse to obey simple things like 'logic' and thus manage to be both a particle and a wave at the same time, and have no mass but some energy; something which should technically be completely impossible.

Basically, Photons are assholes. But they're just the tip of the Quantum Physics Hates You iceburg.

Spoiler: --EDIT-- Found it! (click to show/hide)

[Sean Mirrsen]

I'm waiting for a chance to get back to a meaningful on-topic discussion. No, really.

Spoiler (click to show/hide)

I have nothing better to do by this point. I know nothing of quantum physics, but extrapolating my view on photons at least explains particles "popping in and out of existence" and "being in two places at once". Since a photon particle is the effect of a wavelike energy structure, it would make sense for a single - and essentially, one and the same - photon to appear everywhere along the waveform's peak at once. Same goes for other particles, probably. The universe is filled with all manner of strange waves and vibrations - if any two powerful enough "vibrations" overlap and peak at the same point, the resulting resonance peak will make a particle appear, and wink out of existence when the appropriate conditions pass. This post was not intended to make sense in either conventional or quantum physics as they are known.

[DG]

If would could take a peek at the personalities of the majority here:

INTELLECTUAL_CURIOSITY     91 - 100     Is entranced by riddles and puzzles and loves to debate issues and ideas.

[smjjames]

Um yea...

Spoiler (click to show/hide)

and the vibrations of said quantum particles enables them to synchronize over long distances, allowing FTL speeds, at a quantum scale, at the risk of imploding the universe, or not, or maybe just you turning for the briefest of instants, into a black hole and then back to normal when you are beamed to another place.

I'm just rambling off with nonsense, lol.

Seriously though, I like to debate issues and ideas, just that this whole quantum mechanics and theoretical physics stuff is beyond me.

[Neruz]

I'm waiting for a chance to get back to a meaningful on-topic discussion. No, really.

Spoiler (click to show/hide)

I have nothing better to do by this point. I know nothing of quantum physics, but extrapolating my view on photons at least explains particles "popping in and out of existence" and "being in two places at once". Since a photon particle is the effect of a wavelike energy structure, it would make sense for a single - and essentially, one and the same - photon to appear everywhere along the waveform's peak at once. Same goes for other particles, probably. The universe is filled with all manner of strange waves and vibrations - if any two powerful enough "vibrations" overlap and peak at the same point, the resulting resonance peak will make a particle appear, and wink out of existence when the appropriate conditions pass. This post was not intended to make sense in either conventional or quantum physics as they are known.

Spoiler (click to show/hide)

Good, because it doesn't

And of course, we havn't even started getting into the more exotic fun-filled aspects of Asshole Physics, like Quantum Entanglement.

[G-Flex]

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

That's the point; you can't treat it as one. In order to understand what the expression means, you need to understand how you arrived at "infinity" in the first place. Hence why it's indeterminate.

The zero isn't "more powerful" than the infinity (someone else mentioned this idea). It might seem that way intuitively, but it doesn't make any sense: You can have a limit resolve to 0*∞ and yet it is not necessarily equal to zero; you need to do further analysis.

For another example, a limit resolving to 1^∞ doesn't necessarily equal 1, either.

The basic thing to understand is that once infinity enters the picture, you're dealing with limits and continuity and the rules one is used to might not apply the way you expect them to.

[CobaltKobold]

For another example, a limit resolving to 1^∞ doesn't necessarily equal 1, either.

Should...because
1^x = 1, ∀ x ∈ ℝ
and you do not appear to specify a complexly infinite result.
(It's trivially provable to show
1^x =1  ∀ x ∈ ℚ
but I haven't taken math recently enough to do it for irrationals (board rejects set character) as well, though I suspect something involving the continuity of f(x)=a^x would suit)

[Christes]

Well clearly 1^x=1, but that's not the point.

Take lim_x->∞(1+1/x)^x.  That does not equal 1 - in fact it equals e.  However, it resolves to 1^∞

Also, the term "infinity" (as a noun) is being thrown around a lot.  Can someone actually define what they mean precisely?