# 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 ancient Greeks had such a term for an irrational number:

- The proof that there exist such numbers was a shock to their collective national psyche.

The symbol $\Q$ arises from the construction of the rational numbers as the $\Q$uotient field of the integers $\Z$.

## Sources

- 1971: Allan Clark:
*Elements of Abstract Algebra*... (previous) ... (next): $\S 1$ - 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