Use Definition 1.21 to prove that the set of odd integers iscountably infinite.

Question

Use Definition 1.21 to prove that the set of odd integers iscountably infinite. DEFINITION 1.21: Let A be an arbitrary set. a) The set A is FINITE if it is empty or ifits elements can be put in a one-to-one correspondence with the set{1,2,...,n} for some positive integer n. b) The set A is INFINITE if it is notfinite. c) The set A is countably infinite if itselements can be put in a one-to-one correspondence with the set ofpositive integers. d) The set A is countable if it is eitherfinite or countably infinite. e) The set A is uncountable if it is notcountable. Use Definition 1.21 to prove that the set of odd integers iscountably infinite. DEFINITION 1.21: Let A be an arbitrary set. a) The set A is FINITE if it is empty or ifits elements can be put in a one-to-one correspondence with the set{1,2,...,n} for some positive integer n. b) The set A is INFINITE if it is notfinite. c) The set A is countably infinite if itselements can be put in a one-to-one correspondence with the set ofpositive integers. d) The set A is countable if it is eitherfinite or countably infinite. e) The set A is uncountable if it is notcountable. Let A be an arbitrary set. a) The set A is FINITE if it is empty or ifits elements can be put in a one-to-one correspondence with the set{1,2,...,n} for some positive integer n. b) The set A is INFINITE if it is notfinite. c) The set A is countably infinite if itselements can be put in a one-to-one correspondence with the set ofpositive integers. d) The set A is countable if it is eitherfinite or countably infinite. e) The set A is uncountable if it is notcountable.

Explanation / Answer

Consider the bijection, f, from the positive integers to the set ofodd integers where f(n) = 2n-1

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