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Prove or disprove: If A is a denumerable set and we continue to add new elements to A
Chapter 5, Problem 14(choose chapter or problem)
Prove or disprove: If A is a denumerable set and we continue to add new elements to A, then we will eventually arrive at a set B where |A| < |B|.
Questions & Answers
QUESTION:
Prove or disprove: If A is a denumerable set and we continue to add new elements to A, then we will eventually arrive at a set B where |A| < |B|.
ANSWER:Problem 14
Prove or disprove: If A is a denumerable set and we continue to add new elements to A, then will eventually arrive at a set B where
Step by Step Solution
Step 1 of 3
Given statement is “If A is a denumerable set and we continue to add new elements to A, then will eventually arrive at a set B where
It can be disproved by a counter example.
Consider the set of natural numbers which is a countable set and add the all the elements of N with a negative sign and a 0, the set becomes the set of Integers which is also countable.