Talk:Cantor's isomorphism theorem/GA1
GA Review
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Reviewer: Kusma (talk · contribs) 13:52, 6 June 2023 (UTC)
Planning to review yet another of your maths GA noms, shouldn't take more than a few days. —Kusma (talk) 13:52, 6 June 2023 (UTC)
Section by section review
- Lead: Is temporal logic more important than all the other related results?
- Statement and examples: The claim that the open interval (0,1) is unbounded is going to confuse readers who have seen "bounded" in the context of subsets of the real numbers. Some of the sources call the property "without endpoints", which might be clearer for the beginner. Could you explain (perhaps in a footnote) that you use the order theory definition of boundedness (which is not inherited by subsets), not the more familiar one from the real numbers?
- Any example for the rationals and a subset of the reals should give a monotone increasing continuous function (by density), and any monotone increasing function on the reals will induce an order isomorphism of the rationals to their image. Are there any other interesting known such monotone functions other than Minkowski-?
- The binary strings ending in 1 are a nice example (but of course they can be seen as just the dyadic rationals in (0,1) in disguise).
- Proofs: "It alternates between the two orders for which one it searches for the first missing element" can you try to break this down a little more? As I understand it, we use the enumerations, take the first element that hasn't yet been used, find a partner for it, then do the same for the other order. "Earliest missing element" is a bit more temporal than "the one with the lowest index" or something.
- textbook by Hausdorff: link and mention Grundzüge der Mengenlehre.
- "mechanized in Coq" what does that mean? Say what Coq is.
- Model theory: "The axioms can be formulated logically using either a strict comparison < or a non-strict comparison" that sounds more like a footnote, it is a bit distracting here.
- The words "logical sentence" and "theorem" could be defined slightly more in their model theory meanings.
- Related results: define "dense in each other"? (although there is of course only one thing it could mean).
- "Suslin's problem... its truth" should be something like "The truth of this statement"
- Is there some context for Baumgartner's axiom?
General comments and GA criteria
Took me a bit longer than planned due to RL and other wiki issues popping up (sorry). See above for prose comments, not really a lot to complain about other than the definitions being possibly confusing. Happy with scope and level of detail; source review to follow. —Kusma (talk) 17:03, 9 June 2023 (UTC)
Good Article review progress box
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