3D triangle computer graphics November 30    3

We are given a 3D triangle with vertices $(0,0,0), (5,0,10), (0,20,0)$. What is the $z$ value of the point in the triangle with $x=3, y=1$? How do we find the $z$ value?There is no such point. All the points of the triangle have $x$ coordinates that

the probability of two spy in the same group November 30

I was watching a TV show, and the setting is pretty simple:There are 10 players in total, within them there are 2 "spies", players initially form 2 teams of 5 people, and there are 3 rounds of game, where at the end of each round, we can switch

A Borel subset of a topological space November 30    1

Is every Borel subset of a topological space $(X, \tau)$ either open or closed?I'm thinking that if $B \in \mathcal B(X)$, then there are many possibilities:$B$ is open for $\tau$, or it is the complement of some open set $B$ in $\tau$, and so closed

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