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...It is likely that the next thing that will happen is a very public beta test of the extension on a dedicated test wiki, with a call to developers to systematically improve the usability and scalability of the extension. After that, my recommendation will be that each wiki community is given the choice to deploy this extension or not, with a clearly defined process for making a decision to do so....

A warm front (according to contemporary reliable pressure charts) which is unusually well defined approaching with the mostly clear sky with cumulus clouds on the horizon disappearing as the altostratus opacus comes in. Possibly represents the side of a warm front.

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. An ordinal is then defined to be a transitive set whose members are also transitive. It follows from this that the members are themselves ordinals. Note that the axiom of regularity (foundation) is used in showing that these ordinals are well ordered by containment (subset).

Transfinite induction can be used not only to prove things, but also to define them (such a definition is normally said to follow by transfinite recursion - we use transfinite induction to prove that the result is well-defined): the formal statement is tedious to write, but the bottom line is, in order to define a (class) function on the ordinals

Thus, every ordinal is either zero, or a successor (of a well-defined predecessor), or a limit. This distinction is important, because many definitions by transfinite induction rely upon it. Very often, when defining a function

of ordinals (a collection of ordinals, possibly too large to form a set, defined by some property): any class of ordinals can be indexed by ordinals (and, when the class is unbounded, this puts it in class-bijection with the class of all ordinals). So we can freely speak of the

in the name, this ordinal is countable), which is the smallest ordinal which cannot in any way be represented by a computable function (this can be made rigorous, of course). Considerably large ordinals can be defined below




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11 Gennaio 2022

21:49:23