Question

State, whether the following pairs of sets are equivalent or not:

Set of integers and set of natural numbers.

Answer 1

Step: Check whether the given pair of sets are equivalent
Given: Set of integers and set of natural numbers

A set of integers is $\{...-1,0,1,2,3,....\}$,
which is clearly an infinite set as it has uncoutable number of elements.

A set of natural numbers is {0, 1, 2, 3,......}
which is also an infinite set as it has uncountable number of elements.

As both the sets have same numbers of elements, the two sets are equivalent sets.

Hence, given sets are equivalent.