Mathematics is just assuming some axioms and rules of inference and then
proving theorems that follow from those. There's no restriction except that
it should be consistent, i.e. not every statement should be a theorem. So
you can regard a game of chess as a mathematical theorem or even a Sherlock
Holmes story. You may suppose these things "exist" in some sense, but
clearly they don't exist in the same sense as your computer.
Now I got it.
Only under the* *assumption that space has a Euclidean metric (*You are
assuming the same to oppose*)- which is begging the question. From the
operational viewpoint (There are other viewpoints as you know), all
measurements yield integers (in some units (If you want to keep the same
unit for two measurements as I said you'd encounter the irrational
numbers)). Real numbers are introduced in the Platonic realm to insure that
some integer equations have solutions(At least sometimes those equations
have some real counterparts). Similarly imaginary numbers are introduced to
complete the algebra. They are all our inventions - except some people
think the integers are not.
You're right to some extends, but my point still is a point!
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