### MF43: Reconsidering `functions' in modern mathematics

The general notion of `function' does not work in mathematics, just as the general notions of `number' or `sequence' don't work. This video explains the distinction between `closed' and `open' systems, and suggests that mathematical definitions should respect the open aspect of mathematics. So while we may well define `constant functions', or `linear functions' etc, we cannot at once capture the idea of a `general function'.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. The full playlist is at http://www.youtube.com/playlist?list=PL5A714C94D40392AB&feature=view_all

Length:
09:51