Set A contains the element 1. What other whole numbers must be in set A for it to be closed under addition?
To determine the other whole numbers that must be in set A for it to be closed under addition, we need to consider how addition works and what it means for a set to be closed under an operation.
Closure under addition means that if we take any two numbers from the set and add them together, the result must also be in the set. In this case, set A contains the element 1. So, we need to find other whole numbers that, when added to 1, produce another whole number that is still in set A.
To find the numbers that satisfy this condition, we need to evaluate the expression 1 + n, where n represents every whole number. By doing so, we can check which values of n result in a whole number that is also in set A.
For example, when n = 0, 1 + 0 equals 1, which is already in set A. So, we include 0 in set A.
Similarly, when n = -1, 1 + (-1) equals 0, which is also in set A. Therefore, -1 needs to be included.
By continuing this process and evaluating 1 + n for all whole numbers n, we find that all integers need to be included in set A for it to be closed under addition. The resulting set will be the set of all whole numbers: {..., -3, -2, -1, 0, 1, 2, 3, ...}.