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26 Cards in this Set
- Front
- Back
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Define the term "SET" in mathematics |
A set is defined as a collection of items. Each individual item belonging to a set is called an element or member of that set.
Example: Set - {1,2,3} Element 1, 2, and 3 are all elements of the set above. |
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How can "SETs" be written? |
Example:
A={1, 2, 3, 4, 5, 6, 7, 8, 9} --or-- A={whole numbers greater than 0 and less than 10} --or-- A=k I 0< k < 10, k is a whole number |
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What is "finite set"? |
A set in which the number of elements can be counted. Ex: { 1, 2, 5, 10} has four (4) elements and therefore is considered "finite". |
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What is an "infinite set" in mathematics? |
A set in which the elements cannot be counted. Ex: {1, 2, 3, 4, 5, 6, 7...} |
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Empty Sets/Null Sets |
Are sets that do not contain any elements |
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What are subsets? |
Given two sets A and B, A is said to be a subset of B if every member of set A is also a member of set B.
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What is an intersection? |
An intersection is the elements in common between or amongst multiple sets.
Ex: A={1, 2, 3, 9, 19} & B={3, 9, 19, 21, 25}
"3, 9, and 19" are elements in the intersection of A and B. |
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What is a union? |
A union includes all numbers in the Venn Diagram.
Example: A={1, 2, 3, 4, 5} & B={2, 3, 5, 7}
The union is 1,2,3,4,5,7 |
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Sets are "disjoint" if: |
none of the elements in A match elements of B. |
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What is a "difference" in a cluster of sets? |
The difference of two sets, A and B, written as A – B, is the set of all elements that belong to A but do not belong to B.
Example:
J = {10, 12, 14, 16}, K = {9, 10, 11, 12, 13} J – K = {14, 16}.
**Note that K – J = {9, 11, 13}. In general, J – K K – J.
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What is a "Cartesian Product"? |
Given two sets M and N, the Cartesian product, denoted M × N, is the set of all ordered pairs of elements in which the first component is a member of M and the second component is a member of N.
Ex: M={1,3,5} & N={2,8} Therefore, the "Cartesian Product" is {(1,2),(1,8),(3,2),(3,8),(5,2),(5,8)} |
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What are "Real Numbers"? |
Real numbers consist of any number you have ever seen: positive, negative, square roots, pi, etc. |
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What is a "commutative property" dealing with real numbers? |
The numbers commute, or move: Addition 2 + 3 = 3 + 2 Multiplication 2 × 3 = 3 × 2
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What is an "associative property" dealing with real numbers? |
Addition 2 + (3 + 4) = (2 + 3) + 4 Multiplication 2 × (3 × 4) = (2 × 3) × 4
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What is a "distributive property" dealing with real numbers? |
The first number gets distributed to the ones in parentheses:
2 (3 x 4) = (2 x 3) + (2 x 4) |
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What is an "identity property" when dealing with real numbers? |
IDENTITY PROPERTY
Adding 0 or multiplying by 1 doesn’t change the original value:
Addition 3 + 0 = 3
Multiplication 3 × 1 = 3
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What is an "inverse property" when dealing with real numbers? |
The inverse of addition is subtraction and the inverse of multiplication is division.
Additive Inverse: 3 + (-3) = 0
Multiplicative Inverse: 3 x 1/3 = 1
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Natural Numbers |
Natural numbers are the whole numbers from 1 upwards: 1, 2, 3, and so on ...
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Whole Numbers |
The numbers {0, 1, 2, 3, ...} etc. |
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Integers |
Integers are numbers with no fractional part.
Includes the counting numbers {1, 2, 3, ...}, zero {0}, and the negative of the counting numbers {-1, -2, -3, ...} |
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Rational Numbers |
Any number that can be made by dividing one integer by another. The word comes from "ratio". |
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Irrational Numbers |
A real number that cannot be written as a simple fraction - the decimal goes on forever without repeating. |
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What are "Proper Fractions"? |
Proper fractions are those that the numerator is less than the denominator.
Ex: 2/3; 1/4; 12/17; etc. |
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What are "Improper Fractions" (also known as "Mixed Numbers")? |
A fraction wherein the numerator greater than or equal to the denominator.
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When dealing with odd and even numbers, keep in mind the following when adding: |
even + even = even
odd + odd = even
even + odd = odd |
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When dealing with odd and even numbers, keep in mind the following when multiplying: |
even X even = even
even X odd = even
odd X odd = odd |
