[EM] Richard's frontrunners example

[Richard Moore]

MIKE OSSIPOFF wrote:

> I still haven't heard anyone actually say what the mathematical
> definiton of "if" is. Will it be in a definition of mathematics?
> Won't someone tell me what it is?

I don't know about the word "if" being defined in math except that it's
usage is the same as in logic. But I think logic actually just defines
implication (or inference).  "If A then B" is understood as an equivalent
way of saying "A implies B".

Implication is defined as a logical expression which is true if the
consequent (B) is true for all cases in which the antecedent (A)
is true. That definition doesn't come from a textbook but I think
it's fairly close.

In set theory, which takes us back to the world of math, A would
be a subset of B; i.e., if x is in A, then x is in B.

 -- Richard