- #1
klabatiba
- 1
- 0
Can anyone please give a really explicit proof (omitting no steps) and with as simple words as possible that any infinite set can be writtern as the union of disjoint countable sets?
Thank you.
Thank you.
Cardinality in set theory refers to the number of elements in a set. It is a measure of the size or quantity of a set, and is denoted by the symbol |A|, where A is the set.
The cardinality of a set is determined by counting the number of distinct elements in the set. This means that if there are repeating elements in a set, they are only counted once in the cardinality.
Yes, two sets can have the same cardinality if they contain the same number of elements. For example, the sets {1, 2, 3} and {a, b, c} both have a cardinality of 3.
The cardinality of the empty set, denoted by ∅ or {} is 0. This is because the empty set contains no elements, hence there is nothing to count.
Infinite sets have a concept of "infinity" as their cardinality. This means that they have an uncountable number of elements and cannot be put into one-to-one correspondence with a finite set. For example, the set of all real numbers has a greater cardinality than the set of all natural numbers.