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[CobaltKobold]

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

this "resolves to" you use does not then sound like it is meaningful, unlike equality.

[G-Flex]

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)

I said "a limit resolving to" for a reason.

Example: lim x->0 of (x+1)^(1/x)

lim x->0 of (x+1) = 1
lim x->0 of (1/x) = ∞

So you'd arrive at 1^∞.

However, just plug in really small values for x, approaching zero. The answer doesn't converge on 1, it converges on e.

(0.00001+1)^(1/0.00001) = 2.7183


Basically, if you have x^y and hold x constant as 1, and y evaluates to ∞, then you get 1.
But if you let x vary and hold y constant at ∞, the answer you get depends on from which direction you let x approach 1: You get either ∞ or 0.
Example numerical analysis: 1.0001^9999999 = 1.873 * 10⁴³⁴ (we are obviously approaching infinity), 0.9999^9999999 = 4.829 * 10^-435 (we are obviously approaching zero)
And if you let both x and y vary, you could get pretty much anything, depending on how they vary (such as my previous example).

[zwei]

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)

Does not matter, photon has energy (or is a energy), hence it has mass. Not being proper particle does not mean jack.

You can make object to gain mass by just making it oscilate (and wave-like behaviour is basically just oscilation: does not matter whether you are particle or wave, you still have mass,).

Also, zero and infinity relations and operations are undefined. And for good reason.
Look at this graph:

http://www.wolframalpha.com/input/?i=1%2Fx

As you see, 1/0 can seem to equal to both +infinity and -infinity

1/0 = +inf
1/0 = -inf, hence +inf = -inf. Obviously not true.

Also consider this:
1/0 = +/-inf
1 = +inf * 0 and well as 1 = -inf * 0, lets mutiply by -1
-1 = inf * 0
1 = inf * 0
-1 = inf * 0 = 1

-1 = 1

Also obviously not true. This is what you get when you are not carefull.

inf * 0 cal be shown to equal to any and every number from R. No, zero is not stronger. Infinity is not either. What you falaciously did is to pick one number from R at random and said inf * 0 equals that.

Irony is that you can predict what happens at infinity, but can not work with it:

1/x aproaches zero for x approaching inf. But you can not say 1/inf = 0 because that is not correct as you can get right back to 1 = 0*inf

[SirHoneyBadger]

I was wondering the other day, while watching a show on string theory and alternate universes: How come they don't teach the physics "alphabet" in highschool?


Atleast they didn't do so a million years ago when I was there (that I noticed).

The table of elements, yes. The Greek alphabet I picked up on my own. Spanish and German were easy, and I atleast can muddle my way through Chinese and Japanese, with lots of translation support, but considering that I'm older than Toady One, I've barely even been exposed to this type of formulaic heiroglyphics.

For that matter, I've got a larger background in ancient Egyptian heiroglyphics, than this stuff that's used every day in modern times to explain the Universe I'm living in.

I realize that as an adult, I'm now responsible for my own education, but someone dropped the ball somewhere, and I'm not taking all the blame for it. I should have been forced to learn it by mandate of the State, along with algebra, and knitting.

[CobaltKobold]

ugg. *takes to PMs*

SHB: This is math we're bandying about, not exactly physics. I don't know why they don't teach calculus in highschool by default, though that's when I learned it.

[Dohon]

When I told my browser to open the forum page, I noticed that this thread had 5 new pages. I squeeled with glee and thought Toady had posted an update which caused everyone to debate and praise the Toad and the Threetoe. Only then did I find out that those 5 whole pages were dedicated to either maths or quantum physics. The squeeling stopped.

While it's all nice and interesting, this discussion REALLY needs a seperate topic. It isn't all related and relevant to DF. And this is still a thread where you discuss the progress of the upcoming version. So, please, misters and misses scientists, go create a topic in general discussion and have at it.

[Neruz]

The topic wanders around a bit when there hasn't been a recent update; it's fine, that's what forum topics do. The key is that this one usually doesn't wander for very long, and it gets back on track when a new update comes up.

[KaelGotDwarves]

Heh, at least we know from Toady's other posts that he's still alive and recuperating.

We went 3 days without an update and people were posting "OMG I THINK HE'S DEAD".

hahah

[SirHoneyBadger]

I'd like to point out that we're modern internet forumgoers, not medieval monks. We're here, we're willing to participate, and we're even relatively well-behaved. What more is required of us?

We all want news about Toady One, and I'm sure we'd be happy to talk about the game, in the absence of that, provided the topic is stimulating enough, for enough people. If you don't want us to wander, you simply must give us a reason not to wander. Doesn't even need to be a good reason: This is an internet forum, afterall.

[Footkerchief]

While it's all nice and interesting, this discussion REALLY needs a seperate topic. It isn't all related and relevant to DF. And this is still a thread where you discuss the progress of the upcoming version. So, please, misters and misses scientists, go create a topic in general discussion and have at it.

I'm just resigned to it now.  Mathchat is better than dead-horse suggestions, at any rate.  I can't think of anything dev-related to talk about so I guess I'll just post a link to the Ark Project, which will eventually be the biggest and bestest, but is right now just the most ambitious zoology mod ever.  We're posting big ass lists of animals there, it's pretty cool and taxonomical.

[Sean Mirrsen]

The Ark Project is cool. We need an equally cool Fantasy Ark Project to bring together various magical beasts from all known creation, and balance them together.

[SirHoneyBadger]

Speaking of animals: If anyone's interested, here's a link to one of my mod projects. I haven't counted the entries in a long time, but I'm guessing there's around a thousand? (what I consider to be) vermin-class animals there: http://www.bay12games.com/forum/index.php?topic=36405.msg575381#msg575381

There are some from mythology/legend, but mostly they're real animals right now. I'm probably going to add atleast 250 more, some of which will be based on legendary critters, and others I'll just make up.

I'd like to aim for 2000 (seems like a nice round figure), but that might be a bit of a stretch.

[CobaltKobold]

If we're talking about mods that should be in vanilla in the future, where's that project aiming to collect the numbers for material strengths of materials/rocks (that toady can't find), etc? How's that coming? My meager search skills are not working.

(Not melting/boiling points. That's the Molten Rocks mod.)

[SirHoneyBadger]

I hope it's still going. I think it was starting up--talked about, anyway--shortly before I left.


I don't have the background for it though, sorry. Maybe someone with a degree (or just a deep interest) in structural engineering or metallurgy?


I'm thinking (idly) about starting up a similar weapons mod (there's atleast 20 different types of medieval battleaxes), and just collecting all the different relevant types/styles I can find, that I'd like to see in the game. That's something I could do with relative confidence and accuracy. Don't know about the timeframe for it though. My plate already overfloweth.

[CobaltKobold]

found it...but it seems to not have been touched in a while.