Definition:Rational Number/Linguistic Note

From ProofWiki
Jump to navigation Jump to search

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.

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