Multiplication.

Except when it doesn't. Like, for me this semester, * has stood for "some binary operation". (This has made typing up my homework more challenging.) But usually it's multiplication -- generally when typing, since the multiplication dot can be kind of hard to make show up.

Why would 0^0 ever equal 1? I don't get that.

n^0 where (n != 0) being equal to 1 I can get since:

n^0 == n^(1 - 1) == 1/n * n == 1

But if n == 0, then you get 0/0 which should be "Oh Shit" instead of 1.

Why would 0^0 ever equal 1?

Convenience.

What? You were expecting something mathy?

Teppy, did you just need to understand for curiosity's sake, or do you have a situation that is requiring you to get this mathy (and should we smite it for you, if you do)?

Just curiosity. I had a completely geeky conversation last night with Confusing!Boy (remember him?) about my unholy love of the OED, and somehow that became a conversation about binary numbers, and I even tried to make a joke about binary numbers....and he didn't hang up on me! Keen!

But all morning I've been thinking about binary numbers (instead of thinking about Confusing!Boy, which I think just proves what a nerd I am).

anything raised to the 0 power is 1.

Even 0? How about a cat?

I have zeros, Tep. Can you raise me?

I have zeros, Tep. Can you raise me?

I see your zeros and raise you a cat. (Take my cat, please!)

So, is it wrong to end my paper on Turing with, "which is too bad, because just think of all the cool stuff he could have done if he hadn't died!" I suppose I should think of some serious way to say that, huh?

anything raised to the 0 power is 1.

Even 0? How about a cat?

I have zeros, Tep. Can you raise me?

I didn't make any of those zero-related comments, you know.

Though I'm pretty good at giving people a....rise.

Binary may be easier to figure out.Than confusing guy.

What? You were expecting something mathy?

It's just it seems like it isn't hard to come up with a mathy reason for 0^0 to be 0/0 ickiness, so why go with the unmathy when the mathy is there?

Oh well.

Well, Gud, here's the thing: I've always defined in the opposite direction. That is, the reason I've always justified that a^-1 was equal to 1/a was the same argument you just made, only backwards. That is, a^-1 has to be such that a^-1 * a^1 = a^0 = 1 (by definition), so a^-1 must be 1/a for a ≠ 0 and undefined for a = 0. But then there's no problem allowing 0^0 to be 1, because it's the 0^-1 that's the undefined number in this insoluble equation. That is: undefined * 0 = 1 makes just as much sense as undefined * 0 = undefined.