# On Constructing Functions, Part 5

This post is the fifth example in an ongoing list of various sequences of functions which converge to different things in different ways. Today we have a sequence of functions which converges to 0 pointwise but does not converge to 0 in $L^1$.

# Maximal ≠ Maximum!

Suffixes are important!

Did you know that the words

"maximal" and "maximum" generally do NOT mean the same thing

in mathematics? It wasn't until I had to think about Zorn's Lemma in the context of maximal ideals that I actually thought about this, but more on that in a moment. Let's start by comparing the definitions: