Don't ever rate anything out of 5!!!!!!!!!!

[Limewater]

But that's not even a complicated number. That's equivalent to (e^(pi*i))^(2*x), which simplifies to (-1)^(2*x), which, assuming x is an integer, simplifes to 1.

Why would you assume x is an integer? x is Real. It's a complex exponential.

[dsheinem]

[Dylan]

Perhaps this will shed some light on the situation (Heh, get it? Light? Sometimes I kill myself).

[AppleQueso]

http://bulbapedia.bulbagarden.net/wiki/Catch_rate

this could factor into ratings somehow I'm sure

[MrPopo]

But that's not even a complicated number. That's equivalent to (e^(pi*i))^(2*x), which simplifies to (-1)^(2*x), which, assuming x is an integer, simplifes to 1.

Why would you assume x is an integer? x is Real. It's a complex exponential.

It's still only one of four numbers: 1, -1, i, or -i, because it's -1 to the something.

[Limewater]

But that's not even a complicated number. That's equivalent to (e^(pi*i))^(2*x), which simplifies to (-1)^(2*x), which, assuming x is an integer, simplifes to 1.

Why would you assume x is an integer? x is Real. It's a complex exponential.

It's still only one of four numbers: 1, -1, i, or -i, because it's -1 to the something.

OK, I didn't really look at your simplification earlier. Now I see the problem.

You can't just apply the power property of exponentials willy-nilly when you have a complex numbers involved.

As an example, look at e^(pi*i) and e^(2*pi*i). e^(pi*i) is -1, and e^(2*pi*i) is 1. However, if we apply the power rule, we can write e^(pi*i) as (e^(2*pi*i))^(0.5). This would simplify to 1^0.5, or simply 1. This does not equal -1. This counterexample shows that the power rule does not hold for complex exponentials.

If you're sticking with Real numbers, you're fine, though.

e^(i*r) (where r is a Real number) equals cos(r) + i*sin(r) (Euler's Formula).

So, e^(i*2*pi*x) equals cos(2*pi*x) + i*sin(2*pi*x). For x between 0 and 1, each unique value of x gives a unique point on the unit circle. In this case, the unit circle would be on the complex plane. This is usually denoted with the Real component corresponding to the x axis, and the Imaginary component corresponding to the y axis.

[MrPopo]

Ah hah, did not know that the power rule doesn't apply with complex exponents. I knew e^i*pi as random math trivia and I've seen the Euler's formula proof of how it turns into 1. Looking it again I see how the power rule chokes and dies. You'll have to forgive my gaff; it's been several years since calculus.

[Limewater]

Ah hah, did not know that the power rule doesn't apply with complex exponents. I knew e^i*pi as random math trivia and I've seen the Euler's formula proof of how it turns into 1. Looking it again I see how the power rule chokes and dies. You'll have to forgive my gaff; it's been several years since calculus.

Ha. No problem. I'm just part of the relatively small portion of society who actually see this stuff on a regular basis. Otherwise, I'd have never made the joke in the first place. Come to think of it, I probably shouldn't have made the joke here.

I think I just realized that my real-life associates are nerdier than my online associates. I don't know what to make of that.

[AppleQueso]

This thread is now about advanced math what

[Luke]

Fact: The Big Dipper was once known as The Big Measuring Cup, but slowslow did not approve of 5-Star constellations. That's right, no 5-stars for him.