It then follows by transfinite induction that there is one and only one function satisfying the recursion formula up to and including ?.
42.
Trying to create a general theory, Denjoy used transfinite induction over the possible types of singularities, which made the definition quite complicated.
43.
:: * The Aleph's JackofOz mentioned are just one kind of types of infinities, called ( transfinite ) cardinal numbers.
44.
If the transfinite upper central series stabilizes at the whole group, then the group is called "'hypercentral " '.
45.
And if I can find out what it is, I might be able to get transfinite clock rates on my Turing machine accelerator.
46.
Such a definition is normally said to be by transfinite recursion the proof that the result is well-defined uses transfinite induction.
47.
Such a definition is normally said to be by transfinite recursion the proof that the result is well-defined uses transfinite induction.
48.
Where ? is a transfinite number greater than all integers and ? is an infinitesimal greater than 0 but less than any positive real number.
49.
Of these transfinite numbers, perhaps the most extraordinary, and arguably, if they exist, " largest ", are the large cardinals.
50.
:Perhaps you might be interested in reading my manuscripts refuting Cantor's transfinite theory and Frege's modern logic at this website.
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