ChapterZero

Identities and inequalities are the twin bug-a-boos of mathematics. As Neils Bohr’s younger brother said: “Analysts are mathematicians who spend half their lives looking for inequalities they can’t prove”, or something like that. I can’t say I know enough to agree, but my experience in the real analysis course was that a lot of problems I spent hours trying to prove directly, or using simpler inequalities, my prof tackled in about two lines, using relatively complex inequalities. There are books dedicated entirely to inequalites— none of which I’ll ever read, I hope and believe. Identities are just as bad. You never know when knowing may save your life, so to speak. Of course, I realize the necessity of being proficient in handling both… I just don’t like it. That’s part of the reason I’m so interested in CASes: good ones, IMO, can handle all that for you. And, that’s part of the reason I’m mad that it took me so long to figure out that A=B is all about proving certain types of identities automatically. I’ve know about this book for a while, but I didn’t know what it was about… somebody’s got some ’splaining to do.

Possibly relevant posts:

• Chebyshev’s inequality (continuous, general version) (1/15/2006)
• Binet’s Formula (1/22/2005)
• One direction in Khintchine’s inequality for Rademacher sums (9/26/2008)