Infinite
The word infinity comes from the Latin infinitas or "unboundedness." It refers to several distinct concepts (usually linked to the idea of "without end") which arise in philosophy, mathematics, and theology.
In mathematics, "infinity" is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is a different type of "number" than the real numbers. Infinity is related to limits, aleph numbers, classes in set theory, Dedekind-infinite sets, large cardinals,[1] Russell's paradox, non-standard arithmetic, hyperreal numbers, projective geometry, extended real numbers and the absolute Infinite.
Logic
In logic an infinite regress argument is "a distinctively philosophical kind of argument purporting to show that a thesis is defective because it generates an infinite series when either (form A) no such series exists or (form B) were it to exist, the thesis would lack the role (e.g., of justification) that it is supposed to play."<ref>Cambridge Dictionary of Philosophy, Second Edition, p. 429
- ↑ Large cardinals are quantitative infinities defining the number of things in a collection, which are so large that they cannot be proven to exist in the ordinary mathematics of Zermelo-Fraenkel plus Choice (ZFC).
