And if you get into machine proofs, you find the need to nail all those concepts down.<p><i>"'Equal' is used freely, from kindergarten to postgraduate. It's never defined or explained.</i>"<p>Which is a problem.<p>Uses of "equal" include:<p>- Constraint. "x = y" as "x and y are constrained to have the same value." This is a common algebraic usage.<p>- Definition: "f(x) = x + 1"<p>- Equivalence: "x * 2 = 2 * x"<p>- Assignment: "x = 1"<p>- Comparison: "x = 1"<p>You're supposed to decide from context which usage is meant.<p>MathCAD used to use different symbols for each of these. Not a bad idea. (MathCAD is still around, but PTC bought it and it's now $620 a year.)
> In plain English, "Tea or coffee?" means one or the other, not both. It's called the "exclusive or."<p>And then the followup, "Milk or sugar?" is an inclusive or. English... amirite?<p>Another favourite of mine: pluralization rules. Duck->ducks, mouse->mice, moose->moose.
> Distance is a monotonic increasing function of time, so the inverse function exists.<p>Not to be pedantic, but I think they mean a "strictly increasing" function, as f(x)=1 for x∈ℝ does not have an inverse.