/sci/ - Science & Math

I need a spanning set of the power set [math]\mathcal{P} \{ a,b,c \}, \ K=Z_2 [/math], please could you give me and example? I don't totally get it.

"Consider a nonempty set Z, and a field K, such that [math] K^Z = { f : Z \rightarrow K / f \ is \ a \ function}[/math] and let's define:
[math] + : K^Z × K^Z \rightarrow K^Z, \ (f+g)(x) =f(x) +g(x) \ \forall x \in Z,[/math]
[math] \cdot : K × K^Z \rightarrow K^Z, \ (\lambda \cdot f)(x) = \lambda \cdot f(x) \forall x \in Z.[/math]
Then K^Z is a K-vector space."
I don't fully get this. As far as I get it this means that Z^K are all the functions which goes from Z to K and that fulfill those two conditions, but I can't see what that actually means. I would really appreciate if someone could give me an example and a counterexample of two functions that fulfill those conditions.

These programs are very short and most of their content you can learn it online. Are these even worth the money/time?

>>10608362
She's...adorable?

Is there a fundamental difference between "regular" and "reverse" calculations?
[math]2^3[/math] can be simply be calculated step by step for anyone, but [math]\sqrt[3]{8}[/math] is basically asking "find a number whose cube is 8" which is a bit more tricky apart from the fact that the answer is easy to guess in this particular case. Or consider calculating exponents vs logarithms, differentiation vs integration.