Ross Churchley

Are irrationals unreasonable?

The ancient Greek word for "irrational number" is hard to translate

Numbers like π and 2 are irrational. But does that mean they’re unreasonable or just that they lack a ratio?

The Ancient Greek ἄλογος is even more ambiguous. Λόγος is used by Euclid to mean ratio, but it could also mean word, speech, story, idea, or reason reason. So ἄλογος could also mean speechless, unspeakable, unexpected, or non-reasoning.

Modern Greek mathematicians now call ℚ the inexpressible (άρρητος) numbers.