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(RA02) Axiom of Choice, Zorn's Lemma, and the Well Ordering Principle 1 год назад


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(RA02) Axiom of Choice, Zorn's Lemma, and the Well Ordering Principle

In this video, we explore a few options for our foundational axiom(s). Note that a set of axioms usually is chosen to be the smallest number of assumptions that one needs in order to construct as much as you can from. In particular, we discuss the Axiom of Choice, Zorn's Lemma, and the Well Ordering Principle, all of which are equivalent to one another (i.e. any one of them implies another). During their explorations, we discuss partially ordered sets, totally ordered sets, choice functions, and the differences/similarities between upper bounds, least upper bounds, maximal elements, and maximum elements. -The Let's Learn, Nemo Community- ►YouTube –    / letslearnnemo   ►Discord –   / discord   ►Twitch –   / letslearnnemo   ►Patreon -   / letslearnnemo   ►Website – https://www.LetsLearnNemo.org #LetsLearnNemo #axiomofchoice #zornslemma

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