Exercise 218Logic, sets and proofs › Countability and cardinalityHigh schoolAdded 3 Nov 2026

Cardinality of finite sets

#finite sets#cardinality#bijection

Statement

Define the cardinality of a finite set and compute $|\{a,b,c,d\}|$ and $|\emptyset|$ .

Hint

A finite set has cardinality $n$ if there exists a bijection with $\{1,\ldots,n\}$ .

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Definition. A set $A$ is finite with cardinality $n$ if there is a bijection $A\to\{1,\ldots,n\}$ . The empty set has cardinality $0$ .

Compute. $|\{a,b,c,d\}|=4$ and $|\emptyset|=0$ .

Conclusion. $|\{a,b,c,d\}|=4$ , $|\emptyset|=0$ .