Cardinality: Let A and B be sets. We write A B (and say A has the same cardinality as B) if there is bijection f : A B. We write A < B if there is an injection f : A -→ B. Theorem 1: Let A and B be sets. Then, A B if and only if A < B and B< A. Exercise 2: Let neZ and suppose n > 1. Use Theorem 1 to prove or disprove that N N".

Cardinality: Let A and B be sets. We write A B (and say A has the same cardinality as B) if there is bijection f : A B. We write A < B if there is an injection f : A -→ B. Theorem 1: Let A and B be sets. Then, A B if and only if A < B and B< A. Exercise 2: Let neZ and suppose n > 1. Use Theorem 1 to prove or disprove that N N".

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 25E: Determine whether the set S={1,x2,2+x2} spans P2.

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