Thank you for this concise and highly informative video. I hadnt done math in 20 years, and this was one topic I particularly enjoyed. I really appreciated this refreshing trip to memory lane.
Why do we need to use the fact that the ordinals are too big to be a set? When we keep adding upper bound elements to the chain, it seems you found a chain with no upper bound, which already contradicts the hypotheses of Zorn's lemma (every chain has an upper bound)?
Assuming choice holds doesn't seem off at all. We don't need to know that AC is true. All we need to know is that assuming it true won't lead to any contradictions, and THAT, we know relatively safely, provided we pay attention to what we're doing.
What about 2 3 /\ | | 6 İt is a particular ordered set And every chain (6,2)(6,3)have an upper bound But no maximel for whole set (the relationship is multiplay on (2,3,6)set)
This is good, but it's not an academic paper. Cut the first minute and a half. In a video like this, you need to start at the heart of the issue, not with an introduction. You can go back and provide an introduction as context later. But in video and film, it's generally a bad idea to be slow at the beginning.
I watched the video and unfortunately I found it very unsatisfying. Anything interesting, beyond the definition of poset, is not explained. It is not clear why the concept of an ordinal makes any sense, or what "too large to be a set" means, or what even the axiom of choice is, or why "well ordering" is justified philosophically
I disagree; there is only so much that can be covered in one video on a deep topic. I thought he took a deep topic and boiled it down to an intuitive sense without degrading the facts or discouraging deeper research into or understanding of the actual rigor.
I'm glad your channel exists. Great job on the general rigor in your videos.
I found this video very helpful when learning about the topic in uni. Very well presented and explained, thanks :)
Thank you for this concise and highly informative video. I hadnt done math in 20 years, and this was one topic I particularly enjoyed. I really appreciated this refreshing trip to memory lane.
Why do we need to use the fact that the ordinals are too big to be a set? When we keep adding upper bound elements to the chain, it seems you found a chain with no upper bound, which already contradicts the hypotheses of Zorn's lemma (every chain has an upper bound)?
First I learned about the Xorn monster in Dungeons and Dragons. Now I learn about the proper Zorn. Which is scarier?
Assuming choice holds doesn't seem off at all. We don't need to know that AC is true. All we need to know is that assuming it true won't lead to any contradictions, and THAT, we know relatively safely, provided we pay attention to what we're doing.
What about
2 3
/\
|
|
6
İt is a particular ordered set
And every chain (6,2)(6,3)have an upper bound
But no maximel for whole set
(the relationship is multiplay on (2,3,6)set)
maximal element doesn't mean biggest element
You are great
This is good, but it's not an academic paper. Cut the first minute and a half. In a video like this, you need to start at the heart of the issue, not with an introduction. You can go back and provide an introduction as context later. But in video and film, it's generally a bad idea to be slow at the beginning.
Thanks for the feedback!
I watched the video and unfortunately I found it very unsatisfying. Anything interesting, beyond the definition of poset, is not explained. It is not clear why the concept of an ordinal makes any sense, or what "too large to be a set" means, or what even the axiom of choice is, or why "well ordering" is justified philosophically
I disagree; there is only so much that can be covered in one video on a deep topic. I thought he took a deep topic and boiled it down to an intuitive sense without degrading the facts or discouraging deeper research into or understanding of the actual rigor.
you should zoom in on your writing and pictures. right now they are pretty small on mobile
Also I think you should pause less when talking. it interrupts the flow