Exercise · ZW-COUNTABLE-SET-003 · ★☆☆ Basic
What is a set equipotent to \(\mathbb{N}\) called?
Choose one option.
Show answer
- D. Countably infinite
Explanation
A set equipotent to \(\mathbb{N}\) is both infinite and countable. The other names describe sets with different properties.
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-004 What is an enumeration of a countably infinite set A?
- 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?