A Class Room Logic / Deductive and Inductive, with Special Application to the Science and Art of Teaching

by George Hastings McNair

7. THREE MATHEMATICAL AXIOMS.

Analogous to the three canons treated in “6,” there are certain mathematical axioms which are here stated:

(1) “Things equal to the same thing are equal to each other.”

(2) “One thing equal to and the other thing not equal to the same third thing are not equal to each other.”

(3) “Things not equal to the same thing may or may not equal each other.”

Illustrations of the three axioms:

(1) If x equals 5, and y equals 5, then x equals y.

(2) If x equals 5, and y does not equal 5, then x does not equal y.

(3) If x does not equal 5, and y does not equal 5, then x may or may not equal y.