Chapter 2

• Mathematical Language is the system use to convey mathematical ideas.
• Mathematical Language is precise, concise and powerful. It is a powerful way of expressing complex thought to its simplest form. It is precise and concise for it is associated with accuracy and exactness.
• Mathematical Expression is defined as a finite combination of symbols expressing a certain concept or idea which has an incomplete thought. It cannot be identified if the expression

  is true or false.
• Mathematical Sentence: is defined as a finite combination of symbols expressing a complete thought.
• Set: a well-defined collection of things or objects.
• Roster Method: is when the elements are enumerated and separated by comma.
• Set Builder Notation: used to describe the elements of the set
• Finite Set: is a set which elements are countable,
• Infinite Set: is a set which elements are not countable
• Unit Set: a set with only one element like
• Empty Set: a set with no element.
• Universal Set: contains all the elements of the given set.
• Equal set: two sets which have the same kind and the same number of element.
• Equivalent set: two sets which have the same number of element but of different kind of element.
• Cardinality of a set: is the number of element in a given set,
• Proper Subset:  a subset that contains some of the elements of the given
• Improper Subset: a subset that contains all the elements of the given set
• Joint set: two given sets with common element.
• Disjoint set: two given sets with no common element.
• Union of sets: A set which contains all the elements of the given sets with no repetition of elements.
• Intersection of sets: A set which contains the common elements of the given sets.
• Complement of a set: a set which contains the elements of the universal set but not the element of the given set.
• Difference of a set: is obtained by subtracting the elements of the two given sets.
• Symmetric Difference: is a set which contains the elements of two given sets after taking the common elements of the two given sets.
• Relation: is a set of ordered pairs. It is a relationship between sets of values, like x-values and y-values.
• Function: is a special type of a relation. A special relationship where each input has a single output.
• Domain: first element of the ordered pair, the x
• Range: second element of the ordered pair, the y
• Table of values. It is a table wherein the x is the independent variable and y is the dependent variable.
• Linear Function:  A function is in the form of y = mx + b where b is not equal to zero.
• Quadratic Function: A function in the form of ax2 + bx + c, where a, b, and c are constant. The graph of a quadratic function is a parabola and degree of the variable is 2. 
• Polynomial Function: It is in the form of a0+ a1x + a2x2 a3x3+… anxn where a0,a1,a2,a3,an are all constant. The degree of the variable is greater than 2. \
• Rational Function: It is in the form of a fraction, like a0+a1x+a2x2+a3x3…+anxnb0+b1x+b2x2+b3x3…+bnxn where a0, a1, a2, a3, an and b0, b1, b2, b3…bn are all constants. The function is defined for every x is an element of real number and the denominator should not be equal to zero.
• Exponential Function:  It is in the form of y = ax where a > 0 and a ≠1. The function is defined for every x is an element of real number and its range is a positive real numbers.
• Logarithmic Function:  It is in the form of y = logax, where a and x is constant and a is the base of the logarithm.