Who introduced the word rational number?
Who introduced the word rational number?
mathematical meaning of irrational.
The OED says that we get the word irrational from the Latin word irrationalis, which was used in Latin for both the mathematical and the non-mathematical sense of irrational. It appears that the mathematical senses of both ratio and rational are backformations from irrational.
Euclid called irrational numbers ἄλογος (alogos). Since the word logos in Greek means either word or reason, this would have meant either unsayable numbers or unreasonable numbers. I expect the name originally was intended to mean unsayable numbers; the ancient Greeks used rationals to identify numbers, so an irrational number would have been a number without a name. Furthermore, the word for the mathematical sense of irrational in modern Greek is άρρητος (arretos), which also means unsayable
mathematical meaning of irrational.
The OED says that we get the word irrational from the Latin word irrationalis, which was used in Latin for both the mathematical and the non-mathematical sense of irrational. It appears that the mathematical senses of both ratio and rational are backformations from irrational.
Euclid called irrational numbers ἄλογος (alogos). Since the word logos in Greek means either word or reason, this would have meant either unsayable numbers or unreasonable numbers. I expect the name originally was intended to mean unsayable numbers; the ancient Greeks used rationals to identify numbers, so an irrational number would have been a number without a name. Furthermore, the word for the mathematical sense of irrational in modern Greek is άρρητος (arretos), which also means unsayable
