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Thursday, June 23, 2016
Associative pairing symbols should be symmetric
Two years ago, the "equality" meme started up, with "marriage equality" being the big buzzword. The social-justice entrepreneurs sent out a lot of purple squares with yellow equal-signs (=) on them; they were on lots of cars, especially on models worth more than my car. Not so much now, but they were there then. Some of us dissident-righters were thinking of posting UNequal-signs (≠). The guy who thought that up didn't get the angle right on the crossout, so the idea had to go through a bit of a "Q A" process first. But now I'm wondering - why should it matter?
Math symbols are those in which A * B means "A [blah] B". To take arithmetic as an example, A + B is the same as B + A, and A x B = B x A. Such relations are called associative. The "Greater Than" / "Less Than" pair is different; A > B is clearly opposite from A < B. It matters what side of what symbol you're on.
You'll note that the plus (+) symbol here hints at associativity in that it is symmetric across the vertical axis. The equal symbol is similar. "Greater Than" / "Less Than" hints at non-associativity.
It'd be nice if the mathematicians had thought of this when they developed the minus sign (-). It's not associative. Neither is the divide sign, but I don't think anyone even uses that anymore; for my part since getting into computers I've always used the fraction sign (/).
Anyway, the not-equal sign represents one of the associative processes: if A ≠ B, then B ≠ A. The symbol should be symmetric and, failing that, it shouldn't matter where the strikethrough leans.
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