In mathematics, a set A is Dedekind-infinite if some proper subset B of A is equinumerous to A. Explicitly, this means that there exists a bijective ... Comparison with the usual... · Dedekind-infinite sets in ZF

27 авг. 2014 г. · A set X is infinite if and only if it is equipotent to a proper subset of itself. Here, X is defined to be infinite if |X| is not a non-negative integer. Equivalent definitions of Dedekind-finite sets Dedekind infinite set definition - Mathematics Stack Exchange Second power of an infinite set is Dedekind-infinite Другие результаты с сайта math.stackexchange.com

22 июл. 2020 г. · Definition. A set is said to be Dedekind-infinite if and only if it is equivalent to (at least) one of its proper subsets.

23 нояб. 2020 г. · A set X X is said to be Dedekind infinite if and only if there exists a function f:X→X f : X → X that is injective (1 to 1), but not surjective ...

7 авг. 2024 г. · Defining Dedekind-Infinite Sets · Dedekind-infinite set is an infinite set that contains a proper subset that can be put into a one-to-one ...

28 мая 2022 г. · A set is infinite if it is not finite. The existence of an infinite set is usually given by an axiom of infinity. The main example is the set of natural ...

9 нояб. 2023 г. · A set is called Dedekind-infinite if it has a bijection to one of its strict subset (equivalently if it has a self-injection that is not surjective).

22 мар. 2013 г. · A set A A is said to be Dedekind-infinite if there is an injective function f:ω→A f : ω → A , where ω ω denotes the set of natural numbers.

18 февр. 2024 г. · Amorphous sets are typically presented as examples of infinite sets that are not Dedekind-infinite (i.e. sets A which have injective functions f ...

But the more exciting fact is that any Dedekind infinite set can be turned into a Dedekind algebra. Theorem infinite.5. sfr:infinite:dedekind: thm ...