It is more precise to say you can fit all of existing mathematics that you can actually check. A number whose only classification is that it is real is a nonph

It is more precise to say you can fit all of existing mathematics that you can actually check. A number whose only classification is that it is real is a nonphysical entity. In constructive systems it can not be reasoned about because it can not exist. Something very close to real numbers exists, but situationally. Pi exists because I can describe a procedure to construct it, same for Euler's number.