Timeline for What is a good approach to the question "the real number 2 is the same as the complex number 2?"
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| Apr 10, 2023 at 11:01 | comment | added | LAU | Second part. I'm not a platonist, but i think that one could represents the view of Plato whithout the need for the suposition of a entity for each mathematical construction. One can think that each construction reflects aspects of the real mathematical entities. Some platonists are more in the Pytagorian approach, some not. | |
| Apr 10, 2023 at 10:53 | comment | added | LAU | Yes, you have a good point. This depends of what one call by an "platonic entity". The form of Two cannot be reduced to the quantity two. When i have two symbols, even if they do not relate to the quantity two in its meaning, they have in the own writing the participation in the Two. Any duality in the world participates in the Two. The quantity two participates in the Two (but this does not mean that it exaust all the Two). Both, the real and the complex two have the participation in the Two by the aspect of quantity. | |
| Apr 8, 2023 at 18:48 | comment | added | Conifold | The problem is that it is not just symbolic system of mathematicians that distinguishes 2 and 2+0i, they "participate" in different Platonic settings. That a monomorphism from one to the other can be defined by mathematicians no more proves that they are the same entity than that different constructions of real numbers can be given by mathematicians proves that there are multiple real numbers 2. Quadratic polynomials with real coefficients are even isomorphic to 3D space, that does not mean that a polynomial and a vector it is mapped to are the same Platonic entity either. | |
| Apr 7, 2023 at 21:27 | history | answered | LAU | CC BY-SA 4.0 |