Prove, by induction, that the sum of the angles of a convex n-gon (with n 3) is 180.n 2/

Adequately Defined Variables Variable: A symbol used to represent a particular mathematical or logical entity with a particular value Variable Declaration: A statement stating that a certain symbol will be used to represent a particular mathematical or logical entity Adequately Defined Variables: Variables with unambiguously specified entities and values ◦ Entity Examples: Integer, Real Number, etc. Global vs Local Variables Global Definition: If the declaration of a variable’s entity and the setting of its value is preserved throughout an argument, unless its value is reset by a global redefinition Local Definition: If the declaration of a variable’s entity and the setting of its value is meaningful for only a limited section of an argument, after which the symbol loses the previous definition and must be redefined before it can meaningfully be used again ◦ Example: If­then statements ◦ Note: A variable is not adequately defined if it is only declared in an if­ then statement Congruence (mod n) – congruence: Let n be a positive integer, and suppose that a and b are any integers… ◦ “a is congruent to b modulo n (“a = b (mod n)”) if and only if a – b is an integer multiple of n” ◦ Theorem: “a = (a + n)(mod n) and a = (a – n)(mod n)” ◦ Corollary: “a = (a + bn)(mod n) Statements in Logic  Statement: A sentence that is true or false, but not both