# Slightly crazy mathmatical stuff

#### not_the_dm

##### New member
RedMenace said:
not_the_dm said:
By the non-existent gods! Have you even studied math? Ever? Point has no size and no dimension. Its an imaginary idea. Now, here is something that will entertain those of us who have some knowledge of math:
Enjoy.
That's useful. I made this thread for exactly that kind of thing. To find where I'm wrong and so we can show other the strange world of maths.

also; G[sub]ab[/sub] = ((8ðG)/c^4)*T[sub]ab[/sub]
Work that one out.
[sub]why is pi coming out as a letter I don't recognise...[/sub]

#### JemJar

##### New member
Regiment said:
not_the_dm said:
...by definition a point in space has to take up some room...
No it doesn't. In fact, by definition, a point doesn't take up space.

#### not_the_dm

##### New member
JemJar said:
Regiment said:
not_the_dm said:
...by definition a point in space has to take up some room...
No it doesn't. In fact, by definition, a point doesn't take up space.
Fair enough. I accept that I was wrong, and now I know...

#### xthetenth

##### New member
Yep, basically infinity is totally counterintuitive. There are no gaps between the lines of symmetry because there are infinitely many of them, so it follows that you can't pick two neighboring lines of symmetry with any separation between them (because then, no matter how small the separation, if you extend that degree of separation between neighbors around the entire circle you end up with a finite number of lines of symmetry). So yeah, infinity is infinite, therefore attempting to deal with infinitesimal separations is invalid.

The curvature thing, well, basically, whose definition of a point are you using anyway? Because it's different from the ones the rest of the world uses of a zero-dimensional location, for this very reason. So once we use the normal people definition of a point it doesn't balloon out to infinity and everybody's happy. And circles with infinite radii work, you're confusing the limit of the infinitesimal curvature with the actual curvature. That and the infinite radius gives the infinitesimal curvature enough space to bend the circle back. Basically there you're confusing the limit of something with the thing itself, while limits deal with what it gets ever so close to but never quite reaches.

#### Doctor VonSexMachine

##### New member
The Koch Snowflake: Infinite perimeter, finite area.

Also: A dimension is simply a parameter. We have a standard where we say the first 4 dimensions are length, width, height and time. Temperature is a dimension, so is opacity. So this nth dimension stuff is just for people who don't understand math and think it's something mystical.

#### not_the_dm

##### New member
You see, this is why I put this here. Intelligent people with intelligent answers

@Doctor VonSexMachine Thats like the butterfly of storms in Terry Pratchet's Interesting Times. A butterfly with wings that are ragged and therefore have an infinite perimeter due to the number of vertices.

#### nezroy

##### New member
Doctor VonSexMachine said:
So this nth dimension stuff is just for people who don't understand math and think it's something mystical.
Except that string theory, in particular 11-dimension M-theory, actually does require/predict that those extra dimensions are an integral part of spacetime and are, in fact, spatial. So in not all cases is it simply a representation of another free variable; sometimes this whole nth dimensions stuff actually is kinda "mystical" #### Regiment

##### New member
Soluncreed said:
Aren't there different sizes of infinity? If you have a gumball machine and for every one you take out you put two in and you do this infinitely then you have an infinite amount of gumballs and two times infinity gumballs in the gumball machine. So there is infinity, just different degrees of it.
There does exist a field of infinity studies, about which I know very little (except that it, in a nod to the repetition of Greek letters, uses Hebrew for notation). In most math, though, that sort of holds. It's a concept that comes in handy for limits. For instance, the limit of, say, (X-1)/(2X) can be found by observing that any appreciably large number plus one is still appreciably large, while twice that number is twice as large, therefore the limit of (X-1)/(2x) as X -> infinity is 0.5. You can (sort of) divide one infinity by two infinities and get 1/2 (although any professor would kill you for saying that).

##### New member
Apparently 0! is 1, which doesn't make sense becuase the only proof of this uses n!=n * (n-1)!, so looking at 1!, we have...

1! = 1 * 0!

and because of that they claimed 0! = 1, but using the same logic on 0!...

0! = 0* -1!

THEREFORE, I REFUSE TO BELIEVE IT!!! I PROVED 0! = 0, SUCK IT MATH PEOPLES!!!

#### Lukeje

##### New member
Apparently 0! is 1, which doesn't make sense becuase the only proof of this uses n!=n * (n-1)!, so looking at 1!, we have...

1! = 1 * 0!

and because of that they claimed 0! = 1, but using the same logic on 0!...

0! = 0* -1!

THEREFORE, I REFUSE TO BELIEVE IT!!! I PROVED 0! = 0, SUCK IT MATH PEOPLES!!!
0! is defined to be 1.

#### ninjapenguin981

##### New member
You didn't take into account that it a/b could be 0.

##### New member
Lukeje said:
Apparently 0! is 1, which doesn't make sense becuase the only proof of this uses n!=n * (n-1)!, so looking at 1!, we have...

1! = 1 * 0!

and because of that they claimed 0! = 1, but using the same logic on 0!...

0! = 0* -1!

THEREFORE, I REFUSE TO BELIEVE IT!!! I PROVED 0! = 0, SUCK IT MATH PEOPLES!!!
0! is defined to be 1.
Shhh... That's what they want you to think...

EDIT: Besides, if you think about factorial in general, you would never throw in a 0 in the mix, would you? so why define a 0!?

#### Eclectic Dreck

##### New member
The reason 0! equals something non-zero is because one can express a factoral as an exponent (e.g. 3! can be expressed as 1*4^3 - 3*3^3 + 3*2^3 - 1*1^3). Thus, if 0! is expressed as a similar exponent, it becomes 1*1^0). I suspect there are other proofs, but this result implies that 0! is not an empty set. This proof is inductive and is hardly rigorous however.

#### SnipErlite

##### New member
e^i-pi = -1

Or so xkcd tells me. I'm terrible at math.
It does. If you're a maths geek then the explanation is some serious crazy (but cool) shit.

##### New member
Eclectic Dreck said:
The reason 0! equals something non-zero is because one can express a factoral as an exponent (e.g. 3! can be expressed as 1*4^3 - 3*3^3 + 3*2^3 - 1*1^3). Thus, if 0! is expressed as a similar exponent, it becomes 1*1^0). I suspect there are other proofs, but this result implies that 0! is not an empty set. This proof is inductive and is hardly rigorous however.
Do you know the pattern for this? I wouldn't mind at least seeing it.

#### Kailat777

##### New member
Soluncreed said:
Aren't there different sizes of infinity? If you have a gumball machine and for every one you take out you put two in and you do this infinitely then you have an infinite amount of gumballs and two times infinity gumballs in the gumball machine. So there is infinity, just different degrees of it.
Yes and no. Yes, there are different sizes of infinity (look up 'cardinality'). Suppose after 30 minutes pass, we remove a gumball from your gumball machine and put in 2. Next, after 15 minutes, we again remove one and put in 2. Do the same after 7.5 minutes. Repeat this until a full hour passes. We would have done this an infinite number of times, and you have an infinite number of gumballs. However, we could 'count' the number of gumballs you put in. Thus, you have a 'countably infinite' number of gumballs. Note in this experiment if we instead removed one and put in, say, 5 or 10 (or any other finite number greater than 1), we would still have a way to count the gumballs, thus we still have the same 'size' of infinity (so removing a larger finite number at a time does not get us a different size of infinity). The integers and the rationals are 'countably infinite'.

Note we cannot come up with a rule to count the real numbers (one doesn't exist). That's because the reals are 'uncountably infinite'. It's unknown (and unknowable) if there is a size between the integers and the reals (we note the rationals have the same cardinality as the integers, as mentioned above. For more information, check out the continuum hypothesis, if you're interested). There are other cardinalities, but that's not my area.

#### Tharwen

##### Ep. VI: Return of the turret
Soluncreed said:
Aren't there different sizes of infinity? If you have a gumball machine and for every one you take out you put two in and you do this infinitely then you have an infinite amount of gumballs and two times infinity gumballs in the gumball machine. So there is infinity, just different degrees of it.
That doesn't really work, because you just tried to apply a real world concept (numbers) to an impossible one (infinity).

#### Malcheior Sveth

##### New member
not_the_dm said:
Sorry if this has already been done but I couldn't find anything like it using the search bar so don't kill me. Basically I'm going to put up some odd shit that comes from maths, physics or whatever. You guys can comment on my oddness, the theories and proofs or add your own. So, here we go.

Circles and infinities:

Imagine a circle. Now, as we know, a circle has an infinate numer of lines of symetry, and these lines run from one side of the circle to the other, passing through the center. Now make the circle bigger. As the lines themselves have not moved they are now an infentesimaly short distance apart at the circumference. If you were to continue making the circle bigger the lines get further and further apart. Basically, infinity is not enough. Of course this assumes that circles can even exist. Which they can't. And here's why;

The definition of a circle is an infinate number of points equidistant about a fixed point in two dimentions. Now as by definition a point in space has to take up some room you would need and infinate circumference to fit all the points on. As C=2ðr the radius must also be infinate. If it has an infinate radius then it must be an infinately long straight line, but as all the points are equidistant from a fixed point the ininately long straight line has to meet itself without curving as it is a straight line. But because all things in existance are effected by gravity and have their own gravitational fields, even light, the line would be curved by it's very exsitance.

And Finally 1=2
a = b
a^2 = a*b
a^2-b^2 = a*b-b^2
(a+b)(a-b) = b(a-b)
(a+b) = b
a+a = a
2a = a
2 = 1

[sub][sub]you can have a cookie if you can work out what is wrong with the 2=1 proof.[/sub][/sub]
Points do not necessarily take up space. The Cantor set, an infinite set of points along the interval [0,1] has measure 0. Also, there is an uncountably infinite number of lines of symmetry assigned to the circle, so they are dense no matter how large you make the circle. You don't get "more of them" if you take a larger circle, because they are actually zero distance apart. And you divided by zero in the second proof.

DELETED

#### HarmanSmith

##### New member
Let's make infinity fun with some set theory!
OK, assume that there is a hotel with an infinite number of rooms, each numbered 1, 2, 3, and so on. Now, every room is already occupied when a tour bus with an infinite number of people arrives, all of whom want a room. The hotel manager thinks for a bit, then has an idea! He moves all of the current tenants from their rooms to the room whose number is twice their current one (i.e. the guy in room 1 will move to room 2, room 2 to 4, 3 to 6 etc.). Now, he has another infinite number of rooms to rent out to the tourists!

Alright, students, now a question for you:
Suppose an infinite number of tour buses carrying an infinite number of tourists each. How does the hotel manager accommodate all of them? (No, he doesn't throw some into the street. There is an actual answer)

I have another cool logic puzzle if anyone is interested. Ask and ye shall receive.