Logit and Expit

Logit, or log-odds, is a sometimes useful function for dealing with probabilities in a more intuitive fashion. Expit is its inverse. This was kind of a tricky algebraic proof for me, but I am out of practice... For the following, assume I'm using log() function in base 2, because I'm a programmer.

$logit(p) = log(odds(p)) = log(\frac{p}{1-p}) \\ expit(p) = \frac{exp(p)}{1+exp(p)} = \frac{2^p}{1+2^p}$

In order to prove these are inverses, I am going to prove that

Just let me type

I like typing. Many programmers don't seem to, but that's ok, we still manage to work together. Except I basically have to use Eclipse for work. (Some people use IntelliJ but I've tried it, it's not sufficiently different or better for my work use-case...) And Eclipse frequently gets in the way of me just typing. I know there are things I could do to alleviate it, but I shouldn't have to!

For example, I want to add braces around a lambda to expand it to a more complicated lambda. I move the cursor to the start of the lambda body, type '{', and... I get a '{' at the end of the line. Syntax error, not what I wanted... I'm still not sure how I eventually got my brace there but it totally took me out of my thought processes to solve this error.

Other times, the whole UI will lock up as I'm typing due to the intelli-sense stuff. I type . and try to type the method name, but it locks up. I'm not even pressing ctrl+space to have it autocomplete, it can still lock up. The worst is when it "can't find a completion" and has to pop up a dialog telling me about that after I waited for many seconds, and I know the completion exists, but some issue has made Eclipse unable to find it which usually resolves with some form of restarting/project nuking.