lesson 1 Flashcards
element
a member of a set
ellipse
the punctuation notation of three dots used to show that a set’s elements continue in the same pattern
notation
a list of symbols that represent terms, operations, and ideas in mathematics
set
a collection of objects with common properties or qualities, such as numbers
subset
a set that contains part or all of another set
Sets
Sets are important because they are the basic property of mathematics. You will find sets in any math course you study. In basic terms, a set is a collection of things. For example, socks, shoes, pants, and a shirt are a set. They have something in common: they are all clothes.
Example 1
a.The set of positive even numbers: We cannot write all the even numbers, so we put an ellipse (the three dots) after the last number to show that the even numbers continue on forever.
b.The set of positive odd numbers:
in math, we usually represent sets by capital letters. We could say set A is the set of positive even numbers, so Set B could be the set of positive odd numbers, so
Two sets are equal if they both have the same elements. They may not look equal at first, so we have to look at them carefully.
Example 2
a.
Is set A equal to set B?
Each set has 4 elements.
Each set contains a
The sets are equal.
b.
Is set A equal to set B?
Set A has 5 elements, and set B has 4 elements.
Subsets
If we take some or all of the elements of a set and make a new set, we have formed a subset. A subset contains some or all elements of the original set.
Example 1
a.
Is B a subset of A?
Each element of set B can be found in set A, so B is a subset of A.
b.
B is a subset of A since the one element in B is found in A.
Example 2
a.
D is not a subset, because it contains an element that is not in C.
b.
Is B a subset of A?
B is a subset of A, because A and B have identical elements.
Is A a subset of B?Yes! The elements of B are in A.
A subset contains an equal or lesser number of the same elements as the set.
