is the set of positive integers the same as the set of nonegative integers? explain please
No, the sets of positive integers and nonnegative integers are different.
Positive integers refer to the numbers that are greater than zero and do not include zero. The set of positive integers is denoted by the symbol {1, 2, 3, 4, ...}, where the ellipsis (...) represents an infinite list of numbers continuing in the same pattern.
Nonnegative integers, on the other hand, include zero along with all the positive integers. The set of nonnegative integers is denoted by the symbol {0, 1, 2, 3, 4, ...}.
To grasp the difference between the two, think about whether or not zero is included. In the set of positive integers, zero is not included, so it starts with the number 1. However, in the set of nonnegative integers, zero is included, so it starts with the number 0.
To understand this concept, you can visualize it on a number line. The set of positive integers would only have ticks starting from 1 and moving towards infinity, with no tick at zero. On the other hand, the set of nonnegative integers would include a tick at zero and continue with positive integers.
Therefore, although the two sets share some common elements (the positive integers), they are not the same because the set of nonnegative integers includes zero while the set of positive integers does not.