transfinitely
English edit
Adverb edit
transfinitely (not comparable)
- (manner) In a manner that requires a transfinite number of steps.
- 1999, Thomas Strahm, “First Steps into Metapredictivity in Explicit Mathematics”, in S. Barry Cooper, John K. Truss, editors, Sets and Proofs, Cambridge University Press, page 399:
- We finish this section by briefly addressing how the reduction procedure for described so far can be formalized in the transfinitely iterated fixed point theory of [18] in order to yield conservativity of over with respect to arithmetic statements.
- 2003, Thomas Forster, Logic, Induction and Sets, Cambridge University Press, page 147:
- After we have performed the deletion operation infinitely many times, we can look at what is left and perform the deletion operation on that, and thereby continue the process transfinitely.
- (degree) Of transfinite degree.
- 2004, Lisa Robin Marks, The Axiom of Choice, Berkeley: University of California, page 35:
- The concern was voiced that Zermelo assumed transfinitely many successive choices, where one choice depends upon another, and that this was unacceptable.
- 2014, Ali Sanayei, Otto E. Rössler, Chaotic Harmony: A Dialog about Physics, Complexity and Life, Springer, page 126:
- It was very radical because he also claimed that symmetry is a feature in mathematics and reality that is not just an infinitely accurate property, but a transfinitely accurate one. Like the modern idea of fractals—where we have this Mandelbrot type thinking of everything repeating itself all over again not just infinitely many times, but in such a way that the surface around it is transfinitely large.
