Talk:Beth number

message: What's gimel used for? Is it used interchangeably with beth? Because they look similar? Awmorp 23:26, 7 June 2006 (UTC)
replies: text: I have no idea.  I've never seen it outside of Wikipedia.  — Arthur Rubin |  (talk) 23:59, 7 June 2006 (UTC)

text: I think that gimel numbers are defined analogously to aleph numbers and beth numbers, but with \gimel_{\alpha+1}=\gimel_\alpha^{\mathrm{cf}(\gimel_\alpha)}. However, I'm not aware of any published reference for this, so I've removed the mention of them from the article (which in any case was confusing due to the lack of explanation). --Zundark 08:21, 8 June 2006 (UTC)
thread_title:  Gimel numbers 

message: Any discussion is taking place at Talk:Beth_two#Merge_into_Beth_Numbers. LambiamTalk 17:54, 2 April 2006 (UTC)
thread_title:  Merging Beth2 into this article 

message: Who decided to spell the word as "beth", when it's actually pronounced "bet"? Is there a lot of history for this spelling? Do mathematicians pronounce it like the female name beth? Ariel. (talk) 11:01, 22 January 2008 (UTC)
replies: text: Beth is the traditional English spelling, and is usually pronounced beth in Britain (but, apparently, bayth in America). I would guess that the spelling is based on Tiberian vocalization, but I don't know for sure. It dates from 1650 according to Merriam-Webster - the OED probably has details, if someone feels like checking them. But all this is something that should be covered in the article on the letter, not in this article - mathematicians merely adopted the existing conventions, which long predate the theory of cardinal numbers. --Zundark (talk) 12:49, 22 January 2008 (UTC)
replies: text: So you are saying mathematicians pronounce it the same way as the hebrew pronunciation? Because in that case it should be noted in the article to pronounce it bet or bais (bays), and not like it looks. Ariel. (talk) 13:12, 22 January 2008 (UTC)
replies: text: I concur that the pronunciation is as in the Hebrew, but the spelling I've usually seen is Beth, in spite of the fact that I usually refer to the Hebrew letter as Bet.  — Arthur Rubin |  (talk) 13:56, 22 January 2008 (UTC)

text: At least in America.  — Arthur Rubin |  (talk) 14:03, 22 January 2008 (UTC)

text: No, I wasn't saying that mathematicians pronounce it as in Hebrew, and I don't know how you read my comment that way. Also, the only type of Hebrew I mentioned was Tiberian Hebrew, and in Tiberian Hebrew the pronunciation is beth, so I especially don't see how you read my comment as suggesting bet or bays. I think that the mathematical pronunciation probably varies as much as the non-mathematical pronunciation, and that we therefore can't specify it. But if someone has a good reference for mathematical pronunciation, go ahead and add it to the article. --Zundark (talk) 15:00, 22 January 2008 (UTC)

text: I refer to it as bet too. Faster than Thunder (talk) 23:05, 17 December 2021 (UTC)

text:  I've always heard it "beth" as a cardinal, though I say "bet" for the letter in other contexts. CRGreathouse (t | c) 02:53, 23 January 2008 (UTC)
replies: text: I'm afraid I've heard it pronouced "bayt", but my father speaks Hebrew, as well as working in logic and set theory, so that might be a special case.  My parents still spelled it "Beth", though, when we weren't using the symbol.  — Arthur Rubin |  (talk) 03:01, 23 January 2008 (UTC)
replies: text: Not to worry, mathematicians butcher eastern european surnames with aplomb. Hardly limited to hebrew. linas (talk) 18:15, 21 April 2012 (UTC)

text: Zundark created this page and there are no move logs for this page. Faster than Thunder (talk) 03:00, 14 January 2022 (UTC)
thread_title:  spelling for beth 

message: I am Robert Munafo. I just noticed this article acknowledges me as a source. However, it bears so little relation to the material on my web pages (e.g. Aleph-1, Power set, etc.) that I wonder if the citation is still relevant. I wouldn't mind if it gets removed. I don't know much about the legal requirements of GNU Free Documentation License to be able to decide on my own.  —Preceding unsigned comment added by Mrob27 (talk • contribs) 02:12, 11 February 2008 (UTC)
replies: text: It turns out that the reason for this acknowledgement is that this article is partly derived from the old "Beth two" article, and the original version of that article was based very closely on your page 2 to the Power of C. But none of that old text exists in the current article, so the acknowledgement is no longer relevant. (By the way, your page incorrectly says that aleph_2 is the same as 2c only if GCH holds. But, in fact, it can hold without GCH, as it's much weaker.) --Zundark (talk) 09:25, 11 February 2008 (UTC)

text: You can add  to the top of the page if you like.  It will add a banner to the page asking for citations.  (By the way, welcome; I like your page on big numbers a lot.)  CRGreathouse (t | c) 15:42, 11 February 2008 (UTC)
thread_title:  References 

message: added the definable real numbers to the list of sets with cardinality Beth number#Beth null (i.e. Aleph null). I reverted on the grounds that the definable reals are not a well-defined set. Laurusnobilis reverted me, saying that they were defined in the article on them.
According to the lead of that article, "A real number a is first-order definable in the language of set theory, without parameters, if there is a formula φ in the language of set theory, with one free variable, such that a is the unique real number such that φ(a) holds in the standard model of set theory (see Kunen 1980:153). ... Note that this definition cannot be expressed in the language of set theory itself.".
In order to be able to say that a set is denumerable (i.e. of cardinality Aleph null), it must first be a set. Since there is no way of defining the collection of definable real numbers in the language of set theory, there is no way to use the axiom of separation (or of replacement) to extract it from the real numbers. Furthermore, the collection would vary depending on the model of set theory within which one tried to define it. Also the article itself provides alternative definitions which would lead to different sets, and provides an "unambiguously described number" which cannot be in the set although most people would consider that number to be a definable real number (if the set of such existed).
Thus, as I said, this notion is not well-defined. So I will revert again. JRSpriggs (talk) 10:13, 4 January 2016 (UTC)
thread_title:  Definable real numbers 

message: ב's name in Hebrew is bet, not Beth, so can you replace the 'Beths' with 'bets'? Faster than Thunder (talk) 06:54, 5 December 2021 (UTC)
replies: text: The relevant question isn't what the Hebrew name is but what the English name is, or more specifically, what name is used in English-language mathematics. As discussed in the section above (you've posted there), this is "beth", not "bet". - CRGreathouse (t | c) 04:23, 19 January 2022 (UTC)
thread_title:  'Beth' or 'bet'? 

message: Let’s say that GCH holds on an ordinal x if the only cardinality <=|V[x]| that is greater than all |V[y]| with y < x is |V[x]|. Then is it true the last comment in your Definition section implies  that GCH holds on each limit ordinal x, whether or not it holds on successor ordinals. 2601:589:4B80:14B0:3151:D61C:9B27:F1AA (talk) 17:31, 15 March 2022 (UTC)
thread_title:  GCH on limit ordinals