(P2) Fundamentals of Data Representation Flashcards
What information { } tell you?
Contains the objects within a set.
What is a natural number?
Positive integer (whole number), including 0.
What are natural numbers also known as?
Decimal or base 10.
How is the set or natural numbers defined?
N = { 0, 1, 2, 3… }
How do you indicate that a set is infinite?
…
What is a rational number?
A number that can be expressed as a fraction (also known as quotient).
What are fractions?
Fractions are made up of two integers, with the value being the ratio between the two.
What is the symbol for a rational number?
Q
What is the symbol for a natural number?
N
What category of number set do both natural and integer numbers fall into?
Rational numbers.
What is an irrational number?
Any number that cannot be represented as a ratio of integers because the decimal equivalent would go on forever without repeating.
What category of number set does recurring decimals fall into?
Rational numbers.
Give four examples of irrational numbers
Pi, Root 2, e (Euler’s number), Golden raito.
What is the symbol for irrational numbers?
There is no symbol.
What is the symbol for real numbers?
R
What category do all natural, integer, rational and irrational numbers fall into?
Real numbers.
What is the symbol for an integer?
Z
What is an integer?
A whole number whose value can be positive or negative.
How is the set of integer numbers defined?
Z = { … -3, -2, -1, 0, 1, 2, 3 … }
What is a real number?
Any positive or negative value and can include a fractional part.
What is the defining feature of a real number?
That the fractional part can be any length, allowing the number to represent a measurement to any level of precision or accuracy.
What is an ordinal number?
A number defining the position of something in a series.
What is a cardinal number?
A number denoting quantity.
What number is not a cardinal number?
0
Give three examples of cardinal numbers.
First, second, third.
Give three examples of cardinal numbers.
One, two, three.
Give an example of when an integer could be used.
Used as a counter to keep track of how many times a loop statement is reapeated.
Give an example of when a natural number could be used.
To identify the location of data within data structure.
Give an example of when real numbers could be used.
Used by CNC machines to handle measurements that vary from millimetres to metres and must work to high degrees of accuracy.
What is a set?
A collection of ordered values where each value appears only once.
Draw the set of real numbers table out.
See booklet.
What are the values is a set referred to as?
Elements, objects, members.
What is it called when you define a set?
Set comprehension or set building.
What does the ‘pipe’ mean? ( | )
Such that
What does E mean in a set?
Is a member of
What does ^ mean?
And
How do you read sets?
The set ___ is defined in terms of x such that x is a member of the set of ___ numbers, and x is …
Do infinite sets have cardinality?
No
Why do infinite sets not have cardinality?
Total size of the set is not known.
What is a countable infinite set?
An infinite set that can be counted, however, the end of the is never reached.
Give an example of an infinite set.
Atomic half-life.
What is the cardinality of an empty set?
0
What are the symbols of an empty set?
See booklet.
What is the Cartesian product?
The Cartesian product of two sets is the set of all possible ordered pairs whose first component is a member of the first set and whose second component is a member of the second set.
What is the symbol for a subset?
See booklet.
What is the symbol for a proper subset?
See booklet.
What is a subset?
When all elements of one set are contained in another.
What is a proper subset?
A subset has fewer elements than the other set.
What is the symbol for ‘not a subset’?
See booklet.
What is the symbol for ‘not a proper subset’?
See booklet.
