I've come to realize that 50% of numerical analysis mistakes that I make are due to overusing the approximation 1/(1-x) ~ 1-x

It always works for concentration inequalities, but burns you in fixed pt (its _okay-ish_ in float)

ヽ(⌐■_■)ノ♪♬ @ @gauntlet/🤖Ventures/tldr/Aera \\ ¯\_(ツ)_/¯ Struggling with the nature of randomness \\ main: @gaa \\ /red-bull /defi-research maxi

I don't understand this but seems legit so recasting in case there are other mathcasters

But also, the idea is the following: if |x| < 1, 1/(1-x) = 1 + x + x^2 + …. So you can approximate 1/(1-x) by 1+x if x is small … but this is a numerically fraught approximation depending on your application (great for neural nets, horrible for eigenvalue estimation)