co-trivial ancient concepts

Let’s recall how this PRODUCT got all started–naive to think we are being just open to the real possibility of a pair of maps having the same domain object.  Then somebody with too much time and too little work pointed out the possibility of near encounters with maps–maps to the common domain of the aforementioned pair of maps.  That led us down the memory lane (1 x 0 = 0 vs. 1 x 2 = 2) to the definition of product.

Once we get a hang of deja vu, you feel like walking the same stretch of beach again.  Also plausible is a map from product, but not necessarily to the factors.  This calls for some sitting-up-straight scribbling of map objects, products, factors, and more objects that are not factors.  So, I need to stand-up for a min.

In the meantime, an ancient principle of mathematics holds that a figure is the locus of a varying element.  The varying element, as a single thing, is a single figure or element itself.

-Conceptual Mathematics, page 83

Pop quiz: Try changing a word or two in the above two sentences, while tracing an imaginary line segment from one end point to the other end point of the line.

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