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I'm fully aware of the definitions. I didn't say the definition of irrationals was wrong. I said the definition of the reals is wrong. The statement about quantum mechanics is so vague as to be meaningless.
Come on then, enlighten the average Joe.
Google it? Axiomatic definition, dedekind cuts, cauchy sequences are the 3 typical ones and are provably equivalent.
A rational number is any number expressible by the division of two integers. such that p/q where p and q are integers and q does not equal 0.
A real number is the set of both rational and irrational numbers. Nothing about continuous anything.
It is exactly that though.
Irrationel and rational numbers are both real.
Quantum physics is limited to the quantum, hence the name.
Being continuous is not actually a requirement of being real.