Exercise · ZW-CARDINAL-NUMBER-004 · ★☆☆ Basic
What is the cardinal of the empty set \(\varnothing\)?
Choose one option.
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- A. 0
Explanation
The empty set has no elements, so its cardinal is 0. The value 1 is often confused with the set that contains the empty set.
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-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?
- ZW-CARDINAL-NUMBER-009 If |A|=3, what is |A× A|?