> In plain English, "Tea or coffee?" means one or the other, not both. It's called the "exclusive or."
And then the followup, "Milk or sugar?" is an inclusive or. English... amirite?
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.
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.
And if you get into machine proofs, you find the need to nail all those concepts down.
"'Equal' is used freely, from kindergarten to postgraduate. It's never defined or explained."
Which is a problem.
Uses of "equal" include:
- Constraint. "x = y" as "x and y are constrained to have the same value." This is a common algebraic usage.
- Definition: "f(x) = x + 1"
- Equivalence: "x * 2 = 2 * x"
- Assignment: "x = 1"
- Comparison: "x = 1"
You're supposed to decide from context which usage is meant.
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.)