{X:X is full of baloney}

June 22, 2007 in Notations, Rants, Textbooks

Turning our attention to beginning algebra courses. First of all, the text I’ve been using most recently is called Intermediate Algebra; “intermediate between pre-algebra and actual (university-credit earning) algebra” is the most charitable spin I can put on that. Anyhow, here again, set theory is used so clumsily that it’s hard not to attribute malice to somebody along the line (Hanlon’s Razor notwithstanding).

Consider, then, an abomination like
is a natural number less than .

If we’re going to go around calling a perfectly inoffensive set like out of its name in order to make some point about our notations, we’d be much better off to actually pretend we believed these very notations were actually good for something and write instead
.

Or how about
is a real number and is not a rational number ? Doesn’t it just make you want to, I don’t know, hurl the chalk at something? Actually, I have to admit that I’ve copied this display on several blackboards in my time … but only to illustrate a point (namely, that it was created by enemies of mathematics and that one of course really means
).

The symbols in question () appear in this very section and are used in the exercises.  Though not, of course, in the exercises about “set-builder” notation — no, these have all been carefully contrived to reinforce the reader’s impression that our goal in presenting this material is to make easy things hard by way of the whole ignore-the-point word & symbol mishmosh I’ve just been complaining of.

But then, that brings us to the saddest part of the whole sorry business. We don’t actually need (still less want) these symbols — or the set-builder notation itself! — for whatever follows in the whole rest of the book! And pretty much every 9th-grade-algebra-for-college-students text that’s come out in several (admittedly very short) generations does things in exactly the same way!

I have what feels like a pretty coherent theory of how things got this way (though essentially no idea as to “what, then, are we to do?”).  But I promised myself I’d keep it brief, so I’ll just wave my hands in the direction of The Muddle Machine.

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