Exercise · ZW-COUNTABLE-SET-004 · ★☆☆ Basic
What is an enumeration of a countably infinite set \(A\)?
Choose one option.
Show answer
- C. A sequence \((a_n)_{n\in\mathbb{N}}\) whose terms run through all elements of \(A\).
Explanation
Enumerating \(A\) means giving a sequence that reaches every element of \(A\) at least once. Bijections with \(\mathbb{P}(A)\) or \(\mathbb{R}\) do not exist, and a finite subset does not contain all of \(A\).
Review the concept: Countable set
A set is countable if it is finite or equipotent to \(\mathbb{N}\), that is, if its elements can be listed in a sequence.
\[A \text{ numerable} \iff A \text{ finito} \lor A\sim\mathbb{N}\]
More practice problems: countable set
- ZW-COUNTABLE-SET-001 What does it mean for a set A to be countable?
- ZW-COUNTABLE-SET-002 Which of these sets is countable?
- ZW-COUNTABLE-SET-003 What is a set equipotent to ℕ called?
- ZW-COUNTABLE-SET-005 Is a finite set countable?
- ZW-COUNTABLE-SET-006 Which of these functions is a bijection from ℕ onto ℤ?
- ZW-COUNTABLE-SET-007 Is ℕ×ℕ countable?
- ZW-COUNTABLE-SET-008 Is ℚ countable?
- ZW-COUNTABLE-SET-009 Which statement about subsets of countable sets is correct?