Exercise · ZW-CARDINAL-NUMBER-009 · ★★☆ Intermediate
If \(|A|=3\), what is \(|A\times A|\)?
Choose one option.
Show answer
- D. 9
Explanation
Each element of \(A\) pairs with each element of \(A\), so there are \(3\cdot 3=9\) ordered pairs.
Review the concept: Cardinal number
The cardinal number of a set \(A\) is the least ordinal equinumerous with \(A\). It measures the size of \(A\) and also works for infinite sets.
\[|A| = \min\{\alpha \in \mathrm{Ord} : \alpha \approx A\}\]
More practice problems: cardinal number
- ZW-CARDINAL-NUMBER-001 What is the cardinal of \2,4,6,8\?
- ZW-CARDINAL-NUMBER-002 What is the cardinal of ℕ?
- ZW-CARDINAL-NUMBER-003 What does it mean for two sets A and B to be equinumerous?
- ZW-CARDINAL-NUMBER-004 What is the cardinal of the empty set ∅?
- ZW-CARDINAL-NUMBER-005 What is the cardinal of \1,2,2,3\?
- ZW-CARDINAL-NUMBER-006 What is the cardinal of P(\a,b,c\)?
- ZW-CARDINAL-NUMBER-007 There is an injection from A into B, but no bijection between them. What is the relation between |A…
- ZW-CARDINAL-NUMBER-008 What is the cardinal of the set of integers x with -3≤ x≤ 4?