I am really confused about sets. Could you explain to me if the following are opened or closed sets and why?
(a) the set of even numbers for division.
(b) the set of whole numbers less than 1000 for division.
(c) the set of whole numbers greater than or equal to 1000 for division.
(a) and (c) are open because there is no largest even number or whole number. In addition, 0 is not included in the set (a), since it cannot be a divisor.
(b) is closed because 1 is the smallest whole number.