Homotopy Type Theory UMyn8W7b (Rev #3, changes)

Showing changes from revision #2 to #3: Added | Removed | Changed

Test Rant about school mathematics

testing The stuff “functions” here taught in school mathematics at many levels aren’t functions on a typeTT as presented in type theory, but rather they are partial and/or multivalued “functions”, which are basically just combinatorial directed graphs on TT. In school algebra, the reciprocal function 1x\frac{1}{x} for x:Fx:F in a field FF is a partial function and the square root function x\sqrt{x} is partial and multivalued. In school calculus, the derivative x\frac{\partial}{\partial x} is a partial function on the function type \mathbb{R} \to \mathbb{R} because certain functions are nowhere-differentiable, and the antiderivative 1x 1\frac{\partial^{-1}}{\partial x^{-1}} is multivalued even for the zero function f(x)0f(x) \coloneqq 0.

Revision on March 15, 2022 at 07:08:34 by Anonymous?. See the history of this page for a list of all contributions to it.