Prove that the set of even integers (... -6, -4, -2, 0, 2, 4, 6) is...

 

Transcribed Image Text:

Prove that the set of even integers (... -6, -4, -2, 0, 2, 4, 6) is countable by explicitly finding a bijection between Z" and the set. +1 29 3 4- 54 6 7- +8 b) Describe the bijection in part a) using a formula for fin) where f: (1.2, 3.4....) (-6,-4,-2.0, 2.4.6...). 6. Decide whether the following sets have the same cardinality or not. a) 2" and (x) x is a positive real number) b) Z and (5, 10, 15, 20, 25...) c) (1.3.5.7.9 } and { -6,-4,-2, 0.2, 4.6...) d) (1.4.9, 16, 25.) and (x|x is a rational number) Prove that the set of even integers (... -6, -4, -2, 0, 2, 4, 6) is countable by explicitly finding a bijection between Z" and the set. +1 29 3 4- 54 6 7- +8 b) Describe the bijection in part a) using a formula for fin) where f: (1.2, 3.4....) (-6,-4,-2.0, 2.4.6...). 6. Decide whether the following sets have the same cardinality or not. a) 2" and (x) x is a positive real number) b) Z and (5, 10, 15, 20, 25...) c) (1.3.5.7.9 } and { -6,-4,-2, 0.2, 4.6...) d) (1.4.9, 16, 25.) and (x|x is a rational number)