What ⇔ means
Each statement implies the other: “if and only if.”
Writing P ⇔ Q, where P and Q are statements, says that P implies Q and Q implies P. Logicians call this a biconditional, or logical equivalence: the two statements are true in exactly the same cases, so either can replace the other in an argument.
Test it before you use it. x = 2 ⇒ x² = 4 is true, but x = 2 ⇔ x² = 4 is false for real numbers, because x = −2 also squares to 4. Only write ⇔ once both directions hold.
Where did the iff symbol come from?
It grew out of 20th-century mathematical logic.
The MacTutor history-of-mathematics archive records the single-line ↔ and the double-line ⇔ for logical equivalence in 1933 and 1954 respectively. The double-line form is credited to Bourbaki, a group of mostly French mathematicians publishing under one collective pen name.
Its job was to squeeze the phrase “if and only if” (shortened in writing to “iff”) into one mark. The double lines match ⇒, the one-way implication arrow, so the pair reads as “one direction” versus “both directions.”
Formal and proof-oriented; it signals that both directions were checked, not a casual back-and-forth.
Don't write ⇔ when you have shown only one direction.
What it means when someone sends it to you
2 readingsDon't confuse it with
4Combination ideas
3Questions people ask
3is ⇔ the same as equals
No. ⇔ joins statements that are true under the same conditions; = says two mathematical objects have the same value.
Can I use ⇔ for implication?
No. Use ⇒ or → when only the left-to-right consequence is established. ⇔ needs the reverse too.
why does ⇔ show as a box
Your font lacks it. As of 2026, Unicode names missing font support as the usual cause of boxes, question marks or blanks; switch to a font that includes the arrow.
How to type ⇔
⇔\21D4Codes and encoding1 code points
A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.