Infinite: Difference between revisions
Jump to navigation
Jump to search
Content added Content deleted
OfficialURL (talk | contribs) |
OfficialURL (talk | contribs) No edit summary |
||
| Line 11: | Line 11: | ||
Without the axiom of choice, these may not be equivalent. Sets that are neither finite nor Dedekind infinite are called '''amorphous sets'''. |
Without the axiom of choice, these may not be equivalent. Sets that are neither finite nor Dedekind infinite are called '''amorphous sets'''. |
||
Within [[ZFC]], the existence of infinite sets is guaranteed by the [[axiom of infinity]], which implies the existence of the natural numbers, which can be proven infinite. Without this axiom, infinite sets can't be proven to exist. |
Within [[ZFC]], the existence of infinite sets is guaranteed by the [[axiom of infinity]], which implies the existence of the natural numbers, which can be proven infinite. Without this axiom, infinite sets can't be proven to exist. A model of this theory is provided by the [[hereditarily finite set]]s. |
||
Important kinds of infinite sets include [[countable]] and [[uncountable]] sets. |
Important kinds of infinite sets include [[countable]] and [[uncountable]] sets. |
||