In contrast to the set-theoretic view, the old formulation avoids considering infinite collections, as avoiding the actual infinite was an important philosophical position of earlier mathematicians.
12.
They used two " logical " arguments against an infinite past, the first being the " argument from the impossibility of the existence of an actual infinite ", which states:
13.
This argument depends on the ( unproved ) assertion that an actual infinite cannot exist; and that an infinite past implies an infinite succession of " events ", a word no clearly defined.
14.
Much of " WMCF " deals with the important concepts of infinity and of limit processes, seeking to explain how finite humans living in a finite world could ultimately conceive of the actual infinite.
15.
No, he simply did not equate what most people call " the actual infinite " with God . " He " didn't call it " actual infinite ", but rather " transfinite ".
16.
No, he simply did not equate what most people call " the actual infinite " with God . " He " didn't call it " actual infinite ", but rather " transfinite ".
17.
This argument depends on the ( unproved ) assertion that an actual infinite cannot exist; and that an infinite past implies an infinite succession of " events ", which is a term the argument does not clearly define.
18.
Are you sure ? ok, I bet you are right . . . but my understanding was that the actual infinite was a'real infinity'and transfinite numbers where infinite numbers but only potentially . . . : S .-- Cosmic girl 05 : 02, 28 February 2006 ( UTC)
19.
It neither exists in nature nor provides a legitimate basis for rational thought . . . The role that remain for the infinite to play is solely that of an idea . " Philosopher William Lane Craig argues that if the past were infinitely long, it would entail the existence of actual infinites in reality.
20.
The first, used in calculus, he called the variable finite, or potential infinite, represented by the \ infty sign ( known as the lemniscate ), and the actual infinite, which Cantor called the " true infinite . " His notion of transfinite arithmetic became the standard system for working with infinity within set theory.
