Question

Let A = {all 0,1 sequences starting with 1}. For example (1,1,1,1,0,0,0,0,0,....) is an element of A.

The best way to establish the cardinality of A is to ___.

Answer 1

The best way to establish the cardinality of set A is to use a concept called bijection. A bijection is a one-to-one correspondence between two sets. In this case, we can establish a bijection between set A and the set of positive integers by mapping each 0,1 sequence in A to a unique positive integer.

Step-by-step explanation:

The best way to establish the cardinality of set A is to use a concept called bijection. A bijection is a one-to-one correspondence between two sets. In this case, we can establish a bijection between set A and the set of positive integers by mapping each 0,1 sequence in A to a unique positive integer.

For example, we can map the sequence (1,1,1,1,0,0,0,0,0,...) to the positive integer 1. The sequence (1,1,1,1,1,0,0,0,0,...) can be mapped to 2, and so on.

This bijection shows that set A is countable, which means it has the same cardinality as the set of positive integers. Therefore, the cardinality of set A is aleph-null, symbolized by ℵ0.