Objectives for Section 2

After studying this section you should be able to do the following.

• Recognise and use the terminology: real number; set; element or member of a set; empty set; length of a sequence; empty sequence, ordered pair, n-tuple, Cartesian product.

• Appreciate that use of precise notation such as the use of different types of bracket conveys important information when using formal notation. For example, square brackets [ and ] denote a sequence, while curly brackets { and } denote a set.

• Use and interpret various pieces of notation:

  • curly brackets to denote a set;

    – definition of a set by using a condition;

  • { } to denote the empty set;

  • [ ] to denote an empty sequence;

  • SeqOfX to denote the set of all sequences with members from X;

  • (x, y) to denote an ordered pair or 2-tuple; (x, y, z) to denote a 3-tuple, etc.;

  • X × Y to denote the Cartesian product of the sets X and Y .

• Determine the cardinality of a given set and the length of a given sequence.

• Given i, determine the ith element of a given sequence.

• Be aware of the ASCII character codes.

• Appreciate that some sets are finite and some are not.