= 27d567bc2d48d9f40e9ccc20ea370b15)
Manfred comments on Draft/wiki: Infinities and measuring infinite sets: A quick reference - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (24)
Blorst horst.
I would like it if you paired each "myth" line with an explicit "truth" line that gave the tl;dr for us, maybe even using simple language e.g.
Myth: The cardinalities of infinite sets can be compared like ordinary numbers. Reality: If the axiom of choice is false, you can have one set's cardinality be both larger and smaller than another's
(maybe even a short blurb explaining the axiom of choice's role)
I could still understand you, but it certainly helped that I'd borrowed my friend's topology book over the summer.
Rather than making a big list, some more structure and an actual conclusion to topic #1 would have helped cement things in my brain.
Since this turned out pretty long, you could actually split the topics into separate posts in a series. And with a little editing I would be all for these being top-level posts rather than discussion secion.
Actually without the axiom of choice, one set's cardinality can be neither larger nor smaller than another's.
OK, I have to ask, how exactly did that become visible?
Ah, this is a good idea, especially because the correction you propose is not quite correct. :) It would be neither larger nor smaller. I see I made the mistake there of assuming familiarity with partial orders, which was foolish; I forgot people need to be explicitly introduced to those.
Hm, do you really think that would help? I was trying to more of provide a quick reference of facts, while referring elsewhere for proofs.
Magic. Also, you might have pressed a button.
You can still do that to a large degree, but I think that even for a LW audience it would be helpful to say what it is, state that it was used in the proof, and explain briefly why we should keep both axiom-of-choice-is-true and axiom-of-choice-is-false cases in mind.
What I mean is, did you see it when I accidentally posted it the first time, before I deleted it, or did you somehow see it after I then deleted it (in which case my name would have appeared as "[deleted]"), or were you somehow able to find the old version after I posted the new one?
Saw it the first time, composed first draft of comment then, tried to post and found out it had been deleted, was sad.
I would have gone the other way and abandoned the attempt to arrange things in a list. I.e., I would have made the structure simpler, e.g., sections divided into paragraphs, e.g., no attempt to number anything.