/sci/ - Science & Math

>>12321593
>but A,B are real numbers
No they aren't. They are Euclidean points. By Axiom 4.2.6, points can't be real numbers because points can contain intervals (Thm 3.2.2) but intervals are not numbers. Therefore, a point can't be a number. Numbers are algebraic representations of points (Ax 2.3.11.)

>>12321586
>A and B are elements of R. at the same time, a and b are also elements of R.
Elements of R are only real numbers in the algebraic representation. They are Euclidean points in the geometric representation.