### The Weierstrass *M*-test pun

The Royal Chain Mail Factory had received a large order for battle uniforms. Each uniform consisted of a chain-mail toga and a pair of chain-mail short pants. Their only problem was how long to make the pants: too short and a soldier could be exposed; too long and a uniform would be excessively heavy.

Perplexed by the problem, in the Royal Mathematician. He had a uniform made and tested. The hem on the pants proved to be too short, so he increased it a little bit, then a little more, and then a little bit more, and so on until finally he was able to derive an exact relationship between the trouser-length and the leg-length of the soldier.

The chief tailor was curious. "How did you determine this ratio?" he asked?

"Easy," said the Mathematician. "I just used the Wire-trousers Hem Test of Uniform Convergence."