Thank you. That is the ideal that I strive for.

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]]>Oh, yes, difference of squares is a really good way of doing that. I almost never think to use it, though, for some reason.

(For those who don’t see it, the difference of squares comes from binomials: (a + b) times (a – b) is equal to a^2 – b^2. Really helps with certain problems.)

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]]>Thank you kindly. I’ve admired your ability as a writer for at least as long!

]]>Yes, that’s the one. It’s a fun bit of reasoning, and probably a good way to show how to do some kinds of proof to people. Like, the same form of a proof won’t work for showing there’s no smallest uninteresting positive real number; what is it that positive real numbers have that counting numbers don’t? And it’s always fun to work on logic proofs when the premises are silly. Charles Dodgson (Lewis Carroll) had a nice demonstration of logical fallacies about how, if one is late for one’s train one is running. So if you see someone running, are they late for their train? Not at all; they run because they are being chased by a tiger. Really makes an impression.

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]]>SOMEONE *(glares at upstairs)* had the answer in about 3 seconds by using the difference of two squares. Nerd.

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