patrick.net

Okay, the discussion of why you can't divide by zero is fun but I'm used to teaching it to kids in a much simpler way. And the thing is, children learn why they can't divide by zero, long before they learn about limits. I'm more likely to use division by zero being undefined, as a lead in, to explore limits of say 5/x as x --> 0 than visa versa.

In elementary school kids should be taught:

20/5 = 4 because 4 x 5 = 20

But 20/0 = ? doesn't even make sense. You're saying what do you multiply times zero to get twenty ?

Early in Algebra, bad students who rely only on memory (not understanding) forget which of the following is zero and which is undefined. 0/5 or 5/0. It's simple, do the math.
0/5 = 0 because 0 x 5 = 0. Where as 5/0 is a question that makes no sense, that is, has no answer, since we know multiplication by 0 gives us 0.

I did stick around for the zero to the zero part which was nice. Another reminder to take complex analysis which I never did, but it's on my to do list. I should find a good online class, but it's tough for me to sufficiency motivate myself to do all the exercises without impending exams, so I"m better off in a real class. Even if auditing, pride would come in to it, if I'm taking the exams (as an additional motivator).

This might be actual Math porn. http://ocw.mit.edu/resources/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/part-i/

Excel says it 1/0 is #DIV/0!
I want my money back.

That was a fun video.

meh, the video is just being pedantic.

node.js has the right idea:

% node
> 1/0
Infinity
> 0^0
0
> 1/Infinity
0
> Infinity + 1
Infinity
> Infinity - 1
Infinity

the only time node freaks is when you try to put it on top and bottom:

Infinity / Infinity
NaN

+infinity = -infinity for both axes.

The complex plane is really the surface of a torus!

The game space in Asteroids is also a torus. A tiny astronaut could tell he's in a torus by taking measurements of the internal angles of his triangular ship at various positions, mapping out the curvature of his universe. He could also tell where he was in the universe, at least in which ring cross-section.

Dan8267 says

+infinity = -infinity for both axes

In projective geometry, two parallel lines meet at infinity and that point is the same point in both directions (or at least that's one way to think of it - it's non euclidean)

rando says

% node

> 1/0

Infinity

> 0^0

0

> 1/Infinity

0

> Infinity + 1

Infinity

> Infinity - 1

Infinity

the only time node freaks is when you try to put it on top and bottom:

Infinity / Infinity

NaN

What about 0/0? 0 * infinity?