If many is used for countable things and much for uncountable, is it then much real numbers?
With rational numbers it's clear because they're countable but real numbers are uncountable.
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DrWatson · 70-79, M
I don't think "countable" in the grammatical sense of a "counting noun" and "countable" in the mathematical sense mean quite the same thing.
DrWatson · 70-79, M
@Luke73 Grammar books certainly don't refer to bijections with the natural numbers, so I would say not.
"Number" is a counting noun, and "real" is merely an adjective.
We don't say "how much number". We say "how many numbers". And that is the grammatical convention even if an adjective precedes "number." The actual nature of the set of real numbers doesn't come into consideration at all. I could be talking about "green numbers" without ever defining what I meant by that expression, but the grammatical rule would be unambiguous.
At least, that is the way an English teacher would see it. And it seems to me that mathematicians have followed that convention.
"Number" is a counting noun, and "real" is merely an adjective.
We don't say "how much number". We say "how many numbers". And that is the grammatical convention even if an adjective precedes "number." The actual nature of the set of real numbers doesn't come into consideration at all. I could be talking about "green numbers" without ever defining what I meant by that expression, but the grammatical rule would be unambiguous.
At least, that is the way an English teacher would see it. And it seems to me that mathematicians have followed that convention.