Talk:Sauer–Shelah lemma
Latest comment: 10 months ago by Logicdavid in topic The statement of the lemma is simply unreadable.
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The statement of the lemma is simply unreadable.
editIt currently says: "if F is a family of sets with n distinct elements" - what has n distinct elements? The family F? Each of the sets in F? Neither interpretation makes sense. Moreover, even if they did, there should not be two interpretations to choose from. And indeed, the correct statement is different from either, and hard to guess from what is written here. (Namely, the union of the sets in F should have n elements).
I will attempt to correct this now. Logicdavid (talk) 03:17, 6 June 2023 (UTC)
- Your "correction" made it worse. You made it state that it only applies to sets whose elements are the positive integers from 1 to n. That is ridiculously and unnecessarily restrictive. —David Eppstein (talk) 06:25, 6 June 2023 (UTC)
- I'm sorry if I made it worse, but it seems to me that whether the sets consist of positive integers or other elements is not a big difference, since one can take bijections. On the other hand, it would be nice if the statement has a mathematically correct interpretation. Of course, if you want to worry about which sets are in bijection with ordinals, that would be a reason to object. Is it that? Logicdavid (talk) 23:09, 16 December 2023 (UTC)
- Would you say it's not a big difference to express all counting problems as being about counting sheep, because anything else can be counted by putting it in bijection with a flock of sheep? —David Eppstein (talk) 00:38, 17 December 2023 (UTC)
- Of course I would! Logicdavid (talk) 22:20, 16 January 2024 (UTC)
- Would you say it's not a big difference to express all counting problems as being about counting sheep, because anything else can be counted by putting it in bijection with a flock of sheep? —David Eppstein (talk) 00:38, 17 December 2023 (UTC)
- I'm sorry if I made it worse, but it seems to me that whether the sets consist of positive integers or other elements is not a big difference, since one can take bijections. On the other hand, it would be nice if the statement has a mathematically correct interpretation. Of course, if you want to worry about which sets are in bijection with ordinals, that would be a reason to object. Is it that? Logicdavid (talk) 23:09, 16 December 2023 (UTC)