27.01.26.md (1262B)
1 # 27/01/26 2 3 ## notation 4 5 - a set is an unordered collection of unique things 6 - it can be empty (written as phi) 7 - it can be finite, or infinite, so it can be any length or no length 8 - items in a set are called elements, use the funny E to say a element is in a set 9 - sets can be made from other set, for example 10 - A = {dog, cat mouse} 11 - B = {w E A | w contains the letter o} 12 - B = {dog, mouse} 13 - cardinality means the number of elements in a set 14 - a subset means that all elements of one set are contained within another 15 - subset's can be written with a sideways U operator, and a condition can be given by iff 16 - a proper subset is where you have a subset that is not equal to the parent set 17 - superset is the opposite of subset 18 - set difference is the elements which exist only in set A, and is given by a backslash, or somethings subtract 19 - the cartesian product, makes a new set which contain paired items, of the items from each set 20 - 0 is not in the natural numbers, unless it is N sub 0 21 - R sup + is the positive real numbers, and R sup - is the opposite 22 - see https://www.probabilitycourse.com/chapter1/1_2_2_set_operations.php for an example of the repeated union of sets