Logical challenges with abstract algebra I | Abstract Algebra Math Foundations 214 | NJ Wildberger

While abstract algebra is not as problematic logically as modern analysis, it still suffers from very serious difficulties. In this video we begin laying out some of these logical reefs that we will have to steer clear from. And we look at the first one: which is distinguishing between descriptions, definitions and specifications of abstract algebraic objects.

For example, how do we officially define a group? It turns out that there are distinctly different approaches to answering this, and notably the theory of groups that we build up is highly dependent on which definition we choose.

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[steveellis]

Thanks for the wonderful series which is very much appreciated.

"There is a sort of enthusiasm in all projectors, absolutely necessary for their affairs, which makes them proof against the most fatiguing delays, the most mortifying disappointments, the most shocking insults; and, what is severer than all, the presumptuous judgement of the ignorant upon their designs."

An account of the European Settlements in America (1757), pp. 19-20, in The Works of Edmund Burke in Nine Volumes, Vol. IX. Boston: Little, Brown, 1839.