Math Chp. 2
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A set is a collection of objects from a specified universe. A set can be described verbally, by list, or with set-builder notation.
Where the universe is a rectangle and closed loops inside the universe correspond to sets. Elements of a set are assocaited with points within the loop corresponding to that set.
- the set of elements in the universal set U that are not elements of A.
A is a subset of B if, and only if, every element of A is also an element of B
A is a proper subset of B when AcB, but there must be some element of B that is not also an element of A. A does not equal B
the set of elements common to both A and B
the set of all elements that are in A or B
consists of the objects allowed into consideration for a set (symbol U)
an object that belongs to the collection, or set
Natural number or Counting number
a member of the set (Symbol N)
when A and B have percisely the same elements
A set that has no elements in it and is written O
are tow sets that have no elements in common
(AUB = O)
an example which shows that a statement is false.
The types of numbers
- 1. Ordinal Numbers
- 2. Cardinal Numbers
- 3. Nominal Numbers
Nominal Numbers or Identification
a sequence of digits used as a name or label
ex. an id number
Descires location in an ordered sequence with the words first, second, third, fourth, and son on, communicating the basic notion of "where"
the number of objects in the set, communicating the basic notion of "how many"
ex. there are 9 justices of the U.S supreme court
Equivalence of sets
When there is a one-to-one corresepondence of the elements of the two sets
each element of one set is paired with exactly one element of another set,and each element of either set belongs to exactly one of their pairs
the cardinal numbers of finite sets, with zero bieng the cardinal number of the empty set. they can be represented and visualized by a varitey of manipulatives and diagrams.
Order of the whole numbers
M is less than N if a set with M elements is a proper subset of a set with N elements
a set that is either the empty set or a set wquivalent to (1,2,3...), for some natural number n
a set that is not finite. One way to think of an infinite set is that, if you were to list all memebers of the set the list would go on forever.
Addition of whole numbers
a+b + n(AUB), where as a= n(A), b= n(B)
the sum of two whole numbers is a w hole number
For all whole numbers a and b, a+b= b+a
for all whole numbers a,b,c, a+(b+c) = (a+b) +c
Zero Properts of addition
zero is an additive identity, so a+0 = 0+a=a for all whole numbers a
an operation in which tow whole numbers are combined to form antoehr whole number
Addition or Sum
the total number of a and b combined collection
Addends or summands
the expression a+b are a and b
the unique whole number c such that a =b+c
in the expression a-b...it is a
i the expression a-b it is b
a repeated addition, so that a*b = b+b...+b where the are a addends
each whole number a and b of the product a*b
Repeated addition Model
A way to represent the multiplication operation; where a and b are any two whole numbers, a multiplied by b, written a*b, is defined by a*b = b+b....+b with a addends, when a is not zero and by 0*b
the prepersentation of the first component,a, form one set and a second component, b, from anotehr set. It also indicates the Cartesain coordiantes of a point.
(AxB) the set of all ordered pairs whose first component is an element of set A and whose second componenet is an element of set B
a/b; a is the divedent
a/b; b is the divisor
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