THE SIEVE OF ERATOSTHENES

A useful rule for making  a table of prime numbers is attributed  to another famous Greek astronomer and mathematician, Erastosthenes (c.275-194 B.C.) To find all the prime numbers not greater than n, we write all the integers from 1 to n in a convenient tabulated form; from this table we delete every second number after 2, because they all are divisible by 2, every third number after 3, because they all are divisible by 3, every fifth number after 5, and so on; the numbers which remain after all the deletions are prime numbers less than or equal to n.

SETS

A mathematical set must be defined either by a list, a rule or a formula, so that its elements can be recognized without any doubt or ambiguity. If N is a set, we write n E N meaning that 'n is a member of the set N'. The set of all elements that are being considered in a problem is called the reference set (or universal set), and it is denoted by E or U. The empty set has no elements (compare it with the empty drawer of a desk); it is denoted by O. Any collection of elements of E, ranging from O to E it self, is called a subset of E.