TFAE
Units & Measurements abbreviation · Math
| Stands for | The following are equivalent |
|---|---|
| Categories | Units & Measurements |
TFAE stands for The following are equivalent, a math abbreviation.
Phrase introducing a theorem that lists several statements and asserts that each implies all of the others. Proofs typically show a cycle of implications: (1) implies (2), (2) implies (3), and (3) implies (1).
Example: Let A be an n × n matrix. TFAE: A is invertible; det A ≠ 0; Ax = 0 has only the trivial solution.
Usage notes
Linear algebra's invertible matrix theorem is a famous TFAE list, sometimes running to more than twenty equivalent conditions. Proving a cycle of implications is more efficient than proving every pair separately. The abbreviation is common in lecture notes and textbooks but rare outside mathematics.