Because it sucks to change terminology and pretend ancestors were ignorant because they used different terminology.
Hence, I have replaced "numbers" with "ratios" and "integers" with "numbers" ...
Does this change anything? No. But neither did the original rebranding after Euler.
Now go and watch an otherwise perfectly valid and good video about a Kyoto entrance exam.
A killer question from Japan. Is tan 1° a rational number?
MindYourDecisions | 23 Oct. 2024
https://www.youtube.com/watch?v=9jF6ylBhMOU
PS, there may be contexts in which the question actually does change something.
Not how you calculate with numbers or ratios. But how you think about them philosophically. To St. Thomas, "number" starts with one and builds up by addition, while "space" (and by implication shapes and ratios) starts with one and divides down by divisions and separations. They are not the same. Neither is capable of actual infinity, both are capable of potential infinity, which in addition is called "ad infinitum" and in division is called "infinitesimals" ... btw, modern Mathematics doesn't teach the distinction between "actual" and "potential" .../HGL
PPS, Pythagoreans did not rule Mathematics up to after Euler./HGL
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