zlacker

>>mafaa+(OP)
I recently came accross a math theorem that in my opinion perfectly illustrates how mathematical notation can sometimes reach harmful levels of abuse.

E( E(X|Y) ) = E(X)

This is known as "the law of total expectation", and as a programmer this notation is so weakly typed it makes no sense. The more correct notation is

E_Y(E_X(X|Y))

If you can see that the outer E is summing over Y and the inner one over X, then the theorem is immediately clearer and very intuitive.

>>fouron+XL
My favorite example is from MIT's Intro to Probability and Statistics course:

> Definition: The probability mass function (pmf) of a discrete random variable is the function p(a)=P(X=a).

This only makes sense if you already know what the definition is.