The problem with `functions' | Arithmetic and Geometry Math Foundations 42a

[First of two parts] Here we address a core logical problem with modern mathematics--the usual definition of a `function' does not contain precise enough bounds on the nature of the rules or procedures (or computer programs) allowed.

Here we discuss the difficulty in the context of functions from natural numbers to natural numbers, giving lots of explicit examples. WARNING: this video and the next destabilizes much of the mathematics taught in universities.

This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics.

Video Contents:
00:00 Introduction
04:12 Function F from natural numbers to natural numbers
07:16 More Complicated functions

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My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/...

My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.

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Here are the Wild Egg Maths Playlists (some available only to Members!)

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