As an instructor of mine once said in years past to a fellow student who protested that a point in a proof was “obvious”, “In some sense, the entire subject is obvious. The question is whether or not you’ve proved something.”

The mathematics that you see on this blog will be the kind that requires proofs, real proofs. Aside from Geometry, this will all be what most would consider clearly post-Calculus material, though outside of Analysis, Applied Mathematics, Probability and Statistics, the rationale for requiring Calculus as a prerequisite will almost always look a little shaky. I think that you’ll find that the only nod that I give to Intuitionism comes when I illustrate the proofs. I will never support the notion that a gut reaction is an acceptable substitute for a logical proof, or pretend to be patient with those who would.

If what you see seems to be hair-splitting at times, remember that the universe can surprise us, quite unpleasantly at times, and that in the purer branches of Mathematics, our concern is with the logical connections between abstract concepts, anyway, not with the properties of ink scratches on paper or stacks of pennies.

More later. Somebody’s calling.

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