Ciro Santilli @cirosantilli 35

These feel good. Targeted at upper undergrads, so he says he holds back on some stuff, but gives a good level of detail for people who have a life.

Convergence: math.stackexchange.com/questions/629630/simple-proof-euler-mascheroni-gamma-constant

Same value if you swap any input arguments.

The bioinformatics database: www.ncbi.nlm.nih.gov/

Here's a good example of what you can get out of it: E. Coli K-12 MG1655

Related: en.wikipedia.org/wiki/Protein_(nutrient)

In plain English: the space has no visible holes. If you start walking less and less on each step, you always converge to something that also falls in the space.

One notable example where completeness matters: Lebesgue integral of $L^p$ is complete but Riemann isn't.