Definition:Irrational Number/Linguistic Note

Linguistic Note on Irrational Number
The name irrational number is strictly speaking derived from the fact that such a number cannot be defined as the ratio of two integers.

It is arguable as to whether the name also has connotations of being nonsensical or beyond reason.

The ancient Greeks, whose term for an irrational number was alogon, which evoked a feeling of undesirably chaotic and unstructured, or, perhaps more literally: illogical.