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Exercise 0.3.5 (Tricky): Prove that if A is nonempty and finite, then there exists a unique n N such that there exists a bijection between A and {1,2,3,...,n}. In other words, the notation |A|:= n is justified. Hint: Show that if n>m, then there is no injection from {1,2,3,...,n} to {1,2,3,...,m}.

Exercise 0.3.5 (Tricky): Prove that if A is nonempty and finite, then there exists a unique n N such that there exists a bijection between A and {1,2,3,...,n}. In other words, the notation |A|:= n is justified. Hint: Show that if n>m, then there is no injection from {1,2,3,...,n} to {1,2,3,...,m}.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Exercise 0.3.5 (Tricky): Prove that if A is nonempty and finite, then there exists a unique n N such that there exists a bijection between A and {1,2,3,...,n}. In other words, the notation |A|:= n is justified. Hint: Show that if n>m, then there is no injection from {1,2,3,...,n} to {1,2,3,...,m}.
Transcribed Image Text:Exercise 0.3.5 (Tricky): Prove that if A is nonempty and finite, then there exists a unique n N such that there exists a bijection between A and {1,2,3,...,n}. In other words, the notation |A|:= n is justified. Hint: Show that if n>m, then there is no injection from {1,2,3,...,n} to {1,2,3,...,m}.
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