Infinity And Complements
Discrete Mathematics
Level
2
Suppose \(X \subseteq \mathbb{N}\)
Let \(A\) be the statement that \(X\) contains finitely many elements.
Let \(B\) be the statement that the complement of \(X\), say \(X'= \mathbb{N} \setminus X\) contains infinitely many elements.
Which of the following implications is/are true?
(1): \(A \implies B\).
(2): \(B \implies A\).
Notation: \(\mathbb N \) denotes the set of natural numbers.
by
Wen Z