/sci/ - Science & Math

>>14985204
That's not how expected utility works.
There are two outcomes: winning 100 dollars and not winning 100 dollars. Expected utility is the sum of the probability of each outcome times its payoff.
>>14985268
>Do I need to use the compactness of K for this?
Yes.
>I can't figure out what to do when they're not the same type of open sets as each other.
[math]U \subset X[/math], [math]V = (X - K) \cup \{ \infty \}[/math]
[math]U \cup V = U \cup (X - K) \cup \{ \infty \} = (X - (\overline{U} \cap K)) \cup \{ \infty \}[/math]
Remember that closed subsets of compact sets are also compact.
(Also the question seems to be missing assumptions, I don't think I can assume all compact subsets are closed willy nilly in any topological space)

>>11939787
You had a stupid idea and the audacity to dedicate five years of your life to it, I'm proud of you. Best of luck in whatever you go for next.

>>11684039
>understand intuitively but not rigorously
>>11684325
You can ensure that [math]f(x)[/math] is arbitrarily close to [math]f(x_0)[/math] by making [math]x[/math] sufficiently close to [math]x_0[/math].