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Another great topic is infinite set theory (not just naive set theory as the author mentioned) touching on the transfinite cardinals. Maybe a little advanced,
by davesque 3y ago
Another great topic is infinite set theory (not just naive set theory as the author mentioned) touching on the transfinite cardinals. Maybe a little advanced, but if you can just get to the part where you see how there are different "sizes" of infinity, it can help a lot to understand how infinity is not a number but instead more a way of describing trends in a mathematical process over time. Sort of adjacent to Calculus in the sense of wrangling with infinity, but decidedly different since it's dealing with discrete mathematics.
- kccqzy 3y agoCardinals are either boringly easy or impressively hard. Ordinals are more fun. But yes, let's get the kids started with the basics of cardinals.
- zeroonetwothree 3y agoI’ve always found this area of math a bit navel gazey but if you like it then you might like the book Surreal Numbers by Knuth
- davesque 3y agoI suppose it is. But, to me, that's actually kind of the point. I think a meta lesson of infinite set theory is that logic can lead to strange places. So a practitioner should think of logic as a way to get from point A to point B in conceptual space and not so much as a way of exploring what conclusions are reachable from point A. Actually maybe it's fine to do the latter, but just take what you discover with a grain of salt.