MMW Flashcards
the system of words, signs, and symbols which people use to express ideas, thoughts, and feelings; simple verbal language
Language
system used to communicate mathematical ideas; symbols, numbers, etc.
Mathematical Language
Characteristics of Mathematical Language
- Non-temporal
- Devoid of emotional content
- Precise
Operational Terms and Symbols
- Addition [+] - plus, the sum of, increased by, total, added to, combine, more than
- Subtraction [-] - minus, the difference of, decreased by, subtracted from, diminished, reduced, less than
- Multiplication [x,(),*] - multiplied by, the product of, times of, twice, thrice, of
- Division [÷,/] - divided by, the quotient of, per, half, ratio, out of, split into
consists of terms separated with other term using either plus or minus; combination of numbers and variables using operators
Mathematical Expression
Example of Mathematical Expression
2x + 10
2x + 10
name its parts
2 - numerical coefficient
x - literal coefficient
+ - symbol
10 - constant
The product of three and a number
3 * n
Five times the sum of a number and two
5 ( n + 2 )
how do you read this?
2x + 10
two times a number added to 10
combination of two mathematical expressions using a comparison operator
Mathematical Sentence
what are the comparison operators?
equal, not equal, less than, less than or equal to, greater than, greater than or equal to
signs which convey equality or inequality
relation symbols
the two parts of an equation
members
types of math sentence
- open sentence
- close sentence
it uses variable, meaning that it is not known whether the mathematical sentence is true or false
open sentence
a mathematical sentence that is known to be either true or false
close sentence
two types of close sentence
- True Closed Sentence
- False Closed Sentence
18 > 16.5, 9 is an odd number, 25 ½ = 5 are examples of?
true closed sentence
5 = 1, 9 is an even number, 4 + 4 = 5 are examples of?
false closed sentence
one of the most basic in mathematics
sets
a collection of objects that have something in common or follow a rule
sets
elements listed within a pair of curly brackets { } with no elements repeated
sets
well-defined collection of distinct objects
sets
sets are named in?
capital letters
objects that make up a set and can be numbers, people, letters of the alphabet, other sets, etc. And is usually denoted by a lower-case letter
elements or members
usually used to specify that the objects written between them belong to a set
braces
How to describe a set?
- Roster/Tabular Method
- Rule/Descriptive Method
elements in the given set are listed or enumerated, separated by a comma, inside a pair of braces
Roster/Tabular Method
the common characteristic of the elements is defined; uses set builder notation where x is used to represent any element of the given set
Rule/Descriptive Method
Kinds of Sets
- Null/Void/Empty Set
- Finite Set
- Infinite Set
- Universal Set
has no element and is denoted by ∅ or by a pair of braces with no element inside, i.e. { }
null/void/empty set
has countable number of elements
finite set
has uncountable number of elements
infinite set
the totality of all the elements of the sets under consideration, denoted by U
universal set
Two or more sets may be related to each other:
- equal sets have the same elements
- equivalent sets have the same number of elements
- joint sets have at least one common element
- disjoint sets have no common element
a set every element of which can be found on a bigger set
subset
the first set equals the second set
improper subset
a subset of any given set and is considered an improper subset of the given set
null set
the set itself and the null set
proper subset
set containing all the subsets of the given set with n number of elements; with 2^n number of elements
power set
Operations in Sets
- union of sets
- intersection of sets
- difference of sets
- complement of sets
the smallest set which contains all the elements of both sets; a set whose elements are found in A or B or in both
union of sets
the largest set which contains all the elements common to both sets; a set whose elements are common to both sets
intersection of sets
if A and B are two sets, the difference is given by A – B or B – A, means elements of A not in B; a set whose elements are found in set A but not in set B
difference of sets
the complement of a set is the set of all the elements of U not in the complemented set
complement of sets
