The abbreviation “TFAE” is shorthand for “the following are equivalent”. It is used before a set of equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath conditions (each implies all the others).

In a definition, when one of the conditions is somehow “better” (simpler, shorter, …), it makes sense to phrase the definition with that condition, and mention that the others are equivalent. “TFAE” is typically used when none of the conditions can take priority over the others. Actually proving the claimed equivalence must, of course, be done separately.

Title TFAE
Canonical name TFAE
Date of creation 2013-03-22 12:44:40
Last modified on 2013-03-22 12:44:40
Owner ariels (338)
Last modified by ariels (338)
Numerical id 4
Author ariels (338)
Entry type Definition
Classification msc 00A99
Synonym the following are equivalent