Random Thoughts

[Kernel Sohcahtoa]

I just read a full blown ε-δ proof of the following proposition in my real analysis book: if a function f is differentiable at a point a, then f is continuous at a.  I must say that it was pretty awesome to see how a variant of the triangle inequality established a key relationship between the  forward  and backward statements of the proof, which resulted in a beautiful flow of logical reasoning that eventually produced the desired conclusion.

P.S. I must thank Daniel Solow, Gary Chartrand, and Richard Hammack for their books on proofs, as these tools have helped me appreciate the beauty of mathematics.  Live long and prosper.