Topic 1: Set Notation Flashcards
(26 cards)
What is a natural number?
A natural number is used for counting or ordering. They cannot be negative.
{0,1,2,3,4}
What is an integer?
Integers can be whole positive numbers, whole negative numbers and zero.
{…-3,-2,-1,0,1,2,3,4…}
What is a rational number?
Rational numbers can be written as a fraction a/b, where a are integers and b is not 0.
What do rational numbers include?
All fractions:
Proper fractions smaller than 1 (1/2)
Improper fractions bigger than 1 (6/5)
Mixed numbers (1 1/3)
Any number where:
It has a decimal expansion which is finite
The decimal expansion is non-terminating but has a recurring digit or pattern
8 to the power of -2 (8-2)=
1/82
1 over 8 to the power of 2
What are irrational numbers?
Irrational numbers cannot be written as the fraction a/b where b doesn’t equal 0.
What do irrational numbers include?
Any number where:
The decimal expansion never repeats or terminates (ends)
The decimal expansion is infinite
Examples include the square root of 2 and Pi.
What are real numbers?
Real numbers are the set of irrational and rational numbers, which when put together complete the number line.
What type of number is 0?
Integer, natural, real
What is a mathematical set?
A series a collection of objects which are called members or elements of the set.
How can a set be described as a list?
Using the { } brackets.
For example {George, Imogen, Jenna}
George, Imogen and Jenna are the 3 people who make up the set.
What is LCM?
Lowest common multiple
What is HCF?
Highest common factor
How can sets be described as a rule?
The rule is put in { } brackets.
For example {even numbers between 1&9} is the set of number 2,4,6 and 8.
What are sets often labels with?
A capital letter
What can sets be described as?
Infinite in size
What does … mean in this set A={2,4,8,16…}
Continues in this way
What does the E stand for in this set 2E{2,5,7,9}?
E shows membership or element in a set. In this case it shows that 2 is an element of the set. If there is a line through the E its
shows non-membership.
What does n(E) show?
The number of elements in a set. For example E={1,2,3} so n(E)=3
What is probability?
The chance of something happening or how likely something will happen.
How do you calculate the expected number of successes?
Expected number of successes=relative frequency x numb r of trials
What are mutually exclusive events?
Mutually exclusive events are two (or more) events that cannot happen at the same time.
What are exhaustive events?
Ev nuts that have a limited amount of outcomes (e.g tossing a coin).
What does probability add up to?
1
