Sup

I didn't understand the Wikipedia article. I checked there before making this thread. I also checked Wolfram Mathworld, and it looked surprisingly different from the Wikipedia article. I understood the Wolfram one a bit more, but I still don't really understand why it's used.

Unrelated question:
f(x) = cos(ω*x)
f'(x) = -ω*sin(ω*x)
f''(x) = -ω^2*cos(ω*x)
f'''(x) = ω^3*sin(ω*x)
f^4(x) = ω^4*cos(ω*x)
Etc.

x=0 will cause:
f(0) = 1
f'(0) = 0
f''(0) = -ω^2
f'''(0) = 0
f^4(0) = ω^4

Etc. In fact, the pattern will continue: 0, -ω^6, 0, ω^8, 0, -ω^10...

If f is differentiated infinite times, at its peak, it will have ω^∞ = ∞? I'm not saying, "plug in this" to see if it diverges. Even the sine sequences will have a maximum at ω^n.