Definition:Rational Number/Linguistic Note
Linguistic Note on Rational Number
The name rational number has two significances:
- $(1): \quad$ The construct $\dfrac p q$ can be defined as the ratio between $p$ and $q$.
- $(2): \quad$ In contrast with the concept irrational number, which can not be so defined.
- The ancient Greeks had such a term for an irrational number: alogon, which had a feeling of undesirably chaotic and unstructured, or, perhaps more literally: illogical.
- The proof that there exist such numbers was a shock to their collective national psyche.
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $1$: The Notation and Terminology of Set Theory: $\S 1$
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.2$: Numbers, Powers, and Logarithms