TFAE stands for “the following are equivalent.” This statement is fairly common in mathematical theorems. Why, you may ask? Well, there is a lot of power in being able to do something multiple ways. It gives us options to find one that can best fit our mathematical needs. A very familiar example of equivalency would be the Fundamental Theorem of Calculus, it tells us we can either evaluate the integral or anti-differentiate. A less familiar example is Euclid’s propositions 5 and TFAE: A brief history of the Axiom of Choice Lauren Miller 04/22/2017

TFAE stands for “the following are equivalent.” This statement is fairly common in mathematical theorems. Why, you may ask? Well, there is a lot of power in being able to do something multiple ways. It gives us options to find one that can best fit our mathematical needs. A very familiar example of equivalency would be the Fundamental Theorem of Calculus, it tells us we can either evaluate the integral or anti-differentiate. A less familiar example is Euclid’s propositions 5 and