Zorn’s lemma

This is another rant on Zorn’s lemma. And hopefully the final one. It is something that has puzzled me for more than a year now! In a partially ordered set , let every chain have an upper bound. Why is it not obvious that has a maximal element? The whole concept depends on the followingContinue reading “Zorn’s lemma”

The strange difference between “divergent sequences” in real analysis and abstract algebra

I have been working on Commutative Algebra. A lot of the initial proofs that I’ve come across use Zorn’s lemma. The statement of Zorn’s lemma is simple enough (which I have blogged about before): Suppose a partially ordered set has the property that every chain (i.e. totally ordered subset) has an upper bound in .Continue reading “The strange difference between “divergent sequences” in real analysis and abstract algebra”