Notes on Notation

This post is a living document of various ideas on mathematical notation that I think are interesting. Tuple or Set? I often encounter the situation where I have a collection of mathematical objects whose ordering doesn’t matter. The default is usually to pronounce such a collection to be a tuple, and it’s common to hear people colloquially refer to any collection as a (n-)tuple even if ordering is irrelevant. For example, if you’re computing a Monte Carlo estimate of an expectation, you typically have a collection of samples and calculate their average, but how should you write this?