transfinite in a sentence

Examples

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