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Limit ordinal
Limit ordinal A limit ordinal is an ordinal number which is ... precise terms, we say λ is a limit ordinal if for any α < λ, S ... yet another way, an ordinal is a limit ordinal if and only if it is ... equal to the supremum of all the ordinals below it. The term limit in ...
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Limit cardinal
Limit cardinal In mathematics, limit cardinals are a type of cardinal number ... successor operation defined, we can define a limit cardinal in analogy to that for limit ordinals: λ is a (weak) limit cardinal ...
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Ordinal number
... see ordinal (disambiguation). Commonly, ordinal numbers, or ordinals for short, are numbers used to denote ... with no particular structure on it, the ordinals are intimately linked with the so-called ... there may be infinite increasing sequences). The ordinals are both labels for the elements of ... ordinal is defined by the set of ordinals that precede it: in fact, the most common definition of ordinals identifies each ordinal as the set ...
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Talk:Ordinal number
... transitive, then it isn't ordinal. uncountable ordinals I wonder whether in ZF there is ... a proof the class of all countable ordinals is a set. If no, why every ... it trivial that there are some uncountable ordinals, therefore a least one, that it must ... is a set of all the countable ordinals (you do have to use the axiom ... come up with some alternative coding of ordinals and still use ω ω for ...
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Implementation of mathematics in set theory
... the set of all finite von Neumann ordinals) cannot be shown to exist in NFU ... numbers can be considered either as finite ordinals or finite cardinals. Here we consider them ... for the set of finite von Neumann ordinals to exist in NFU, but this strengthens ... use Scott's trick to define the ordinals in essentially this way nonetheless, but instead ... there cannot be a set of all ordinals. In fact, the von Neumann ordinals ...
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Talk:Infinity
... wrong: Infinitum in latin is not without limit but it is without end or not ... for the real numbers, different in general) limit notation, even when no compactification is involved ... part can't be defined cardinals and ordinals, of course various other things like finite ... number (opps ... extended-real) and as a limit is not clear. In my opinion it ... point out that when infinity is a limit you could not treat it as ...
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Talk:Cantor's diagonal argument
... concept of an infinite set, of a limit, or even how to count, nor understand ... a2,a3. . aw}, where aw is the limit of the seq. a1,a2,a3. . ,all ... in N).Then, by the uniqueness of limit of the seq. D1,D2,D3. . ,D ... above. First it says aw is the limit, but there's no reason given to think there is any limit: most sequences do not converge to ...
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Talk:Monty Hell problem
... than zero (not to mention increasing without limit) gives us zero at infinity when analyzed ... to write it in LaTeX) is the limit as t -> infinity of the sum of ... time t. This is not a difficult limit to calculate, since it's precisely (identically ... math>M(t) = 9t. In the limit this is |
Talk:Controversy over Cantor's theory/Archive1
... as I can tell, it's transfinite ordinals that offend Dave. --noösfractal 09:00, 6 ... you allowing these "computations" to take arbitrary ordinals as inputs, or something like that? If ... described by "computation", given that, in general, ordinals can't be thus described (for the ... sense of "computation"), and of course all ordinals are in L. I wanted Barnaby to ... preceding sentence, Poincare proposes a cure - to limit the entities in mathematics to those ...
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Talk:Controversy over Cantor's Theory/Archive1
... as I can tell, it's transfinite ordinals that offend Dave. --noösfractal 09:00, 6 ... you allowing these "computations" to take arbitrary ordinals as inputs, or something like that? If ... described by "computation", given that, in general, ordinals can't be thus described (for the ... sense of "computation"), and of course all ordinals are in L. I wanted Barnaby to ... preceding sentence, Poincare proposes a cure - to limit the entities in mathematics to those ...
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