/sci/ - Science & Math

>>15044134
To prove that any two functions are equal you need to show that they have the same domain and that they have the same values over that domain.

(i) The domain of [math]g[/math] is [math]A[/math] and the domain of [math]g_X[/math] is also [math]A[/math] so these functions indeed have the same domain

(ii) now let [math]z \in A[/math], if [math]z \in X[/math] then [math]g(z)=0=g_X(z)[/math], and if [math]z \notin X[/math] then [math]g(z)=1=g_X(z)[/math], therefore [math]g(z)=g_X(z)[/math] for all [math]z \in A[/math] so these functions indeed have the same values over their domain.

From (i) and (ii) we have [math]g = g_X[/math].

>>14952034
/sci/ is my main board, not /g/
>>14951960
Make sure It's "Introduction to Set Theory" not just "Set Theory", the former is a introductory text and the latter is a reference book.

Also i'm not as good in math as you think i am.