Definition:Biconditional/Notational Variants
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Definition
Various symbols are encountered that denote the concept of biconditionality:
| Symbol | Origin |
|---|---|
| $p \iff q$ | |
| $p\ \mathsf{EQ} \ q$ | |
| $p \equiv q$ | 1910: Alfred North Whitehead and Bertrand Russell: Principia Mathematica |
| $p = q$ | |
| $p \leftrightarrow q$ | |
| $\operatorname E p q$ | Łukasiewicz's Polish notation |
It is usual in mathematics to use $\iff$, as there are other uses for the other symbols.
Sources
- 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S \text{II}.13$: Symbolism of sentential calculus
- 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 1$: Some mathematical language: Connectives
- 1972: Patrick Suppes: Axiomatic Set Theory (2nd ed.) ... (previous) ... (next): $\S 1.2$ Logic and Notation
- 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $2$ Arguments Containing Compound Statements: $2.4$: Statement Forms
- 1980: D.J. O'Connor and Betty Powell: Elementary Logic ... (previous) ... (next): Appendix
- 1988: Alan G. Hamilton: Logic for Mathematicians (2nd ed.) ... (previous) ... (next): $\S 1$: Informal statement calculus: $\S 1.1$: Statements and connectives
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): biconditional (in logic)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): biconditional (in logic)