
Math Lingo vs. Plain English: Double Entendre (1997) - merraksh
http://www.cut-the-knot.org/language/hersh.shtml
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Animats
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.)

~~~
gnulinux
I think you're onto something. When you formalize math you suddenly see how
things summarized to one word or even implied implicitly can require pages of
proof. But in this particular case, you're a little off. At least in
conventional theorem proving (Coq, HOL, Agda) you mostly need 2 of those
("definition" and "equivalence") and for meta programmatic heuristic purposes
(to help the solver) "constraint" too (except this has nothing to do with
"proof proper").

Assignment isn't really needed for formal proofs since assignments usually
requires a computational context that's not pure and most proofs are done
tactics-like or functional style. I also can't see how "comparison" any
different than "equivalence".

I would say the notion of "=" isn't the biggest difference here. I think what
bugs people about "=" in automated proof systems is because (somehow?) our
brain is really good at graph searching mathematical proofs and so typing
equality proof in Coq, Agda, HOL is inherently too verbose.

Sorry to nitpick but this is an important topic as equality-reasoning is one
of the harder parts of automated proof systems.

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lodi
> 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.

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trombonechamp
> 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.

