2.  A sequence is a list of objects arranged in a specific order.  A sequence in computer science is known as an array. An array hold objects of the same type  It may be a finite list, containing a specific number of elements or it may be an infinite list.  The elements may be different or they may be repeated.

3.  Recursive: refers to a previous term 3,8,13,18,23 5 is added to each term to get the next term  Explicit: tells what value a particular term has and is not dependent on the previous number.

4.  A list of squares called b. b contains: 1 as a term 4 as a term 9 as a term Subscripts are used to indicate the position of a term in a list. b 1 =1 2 b is the name of the list, 1 is the position of the term, the value of the term is 1 2 b 2 =2 2 b is the name of the list, 2 is the position of the term, the value of the term is 2 2

5.  The formula for the square list is: b n =n 2 b 1 =1 2 b 2 =2 2 b 3 =3 2 b 4 =4 2 b 5 =5 2 The subscript on the left and the value of n on the right are the same

6.  List a 3, 8, 13, 18, 23 a 1 a 2 a 3 a 4 a 5 Formula for this list: A n =A n-1 + 5 where A 1 =3 A is the name of the list, n is the subscript, A n-1 refers to the previous term in the list.

7.  A 1 =3  A 2 =A 2-1 +5 A 2 =A 1 +5 A 2 =3+5 A 2 =8  A 3 =A 3-1 +5 A 3 =A 2 +5 A 3 =8+5 A 3 =13  A 4 =A 4-1 +5 A 4 =A 3 +5 A 4 =13+5 A 4 =18  A 5 =A 5-1 +5 A 5 =A 4 +5 A 5 =18+5 A 5 =23

8.  Corresponding set is the set of all distinct elements in the sequence. Given the sequence/list: 5,6,5,6,5,6 The set corresponding to the sequence is {5,6}. Given the set {a,b} you could have many kinds of seqeunces. One example would be a,a,b,b,a,b,b,b,a

9.  Characteristic function is denoted f  In binary code, you have a series of 1’s and 0’s 1 represents on or yes 0 represents off or no  The characteristic function of s, of x, = 1 written: fs(X)=1 If X is an element of S, the outcome is 1 If X is not an element of S, the outcome is 0 fs(X) = 0

10.  Universal set U={1,2,3,4,5,6} subset A = {1,2} subset B = {2,4,6} subset C = {4,5,6} The universal set has 6 terms. When we compare A to U, the result will have 6 terms When we compare B to U, the result will have 6 terms When we compare C to U, the result will have 6 terms.

11.  The characteristic function of a = 110000 written: f A = 110000 U={1,2,3,4,5,6} A={1,2} fA(1) is 1 an ∈ of A -> Yes fA(1) = 1 fA(2) is 2 an ∈ of A -> Yes fA(2) = 1 fA(3) is 3 an ∈ of A -> No fA(3) = 0 fA(4) is 4 an ∈ of A -> No fA(4) = 0 fA(5) is 5 an ∈ of A -> No fA(5) = 0 fA(6) is 6 an ∈ of A -> No fA(6) = 0 f A = 110000

12.  U={1,2,3,4,5,6} B={2,4,6} fB=010101  U={1,2,3,4,5,6} C={4,5,6} fC=000111

13.  Regular expression (RE): A regular expression over set A is a string created from elements of A.  RE1: The symbol ∧ (meaning empty string) is a regular expression. An empty string is contained in the set and is a regular expression  RE2: if X ∈ A, the symbol X is a regular expression. The elements of the set are considered regular expressions.  RE 3: if and β are regular expressions, then the expression β is regular. In other words, if the elements are in the set and they are next to each other, the expression is considered regular.  RE4: if β are regular expressions ∨ β is regular. ∨ means join.

14.  RE5: if is a regular expression * (* means finite sequence) is regular. A*: the set of all finite sequences of elements of A *: the set of all finite sequences of elements of