(P2) Fundamentals of Data Representation

Question 1

What information { } tell you?

Answer 1

Contains the objects within a set.

Question 2

What is a natural number?

Answer 2

Positive integer (whole number), including 0.

Question 3

What are natural numbers also known as?

Answer 3

Decimal or base 10.

Question 4

How is the set or natural numbers defined?

Answer 4

N = { 0, 1, 2, 3… }

Question 5

How do you indicate that a set is infinite?

Answer 5

…

Question 6

What is a rational number?

Answer 6

A number that can be expressed as a fraction (also known as quotient).

Question 7

What are fractions?

Answer 7

Fractions are made up of two integers, with the value being the ratio between the two.

Question 8

What is the symbol for a rational number?

Answer 8

Q

Question 9

What is the symbol for a natural number?

Answer 9

N

Question 10

What category of number set do both natural and integer numbers fall into?

Answer 10

Rational numbers.

Question 11

What is an irrational number?

Answer 11

Any number that cannot be represented as a ratio of integers because the decimal equivalent would go on forever without repeating.

Question 12

What category of number set does recurring decimals fall into?

Answer 12

Rational numbers.

Question 13

Give four examples of irrational numbers

Answer 13

Pi, Root 2, e (Euler’s number), Golden raito.

Question 14

What is the symbol for irrational numbers?

Answer 14

There is no symbol.

Question 15

What is the symbol for real numbers?

Answer 15

R

Question 16

What category do all natural, integer, rational and irrational numbers fall into?

Answer 16

Real numbers.

Question 17

What is the symbol for an integer?

Answer 17

Z

Question 18

What is an integer?

Answer 18

A whole number whose value can be positive or negative.

Question 19

How is the set of integer numbers defined?

Answer 19

Z = { … -3, -2, -1, 0, 1, 2, 3 … }

Question 20

What is a real number?

Answer 20

Any positive or negative value and can include a fractional part.

Question 21

What is the defining feature of a real number?

Answer 21

That the fractional part can be any length, allowing the number to represent a measurement to any level of precision or accuracy.

Question 22

What is an ordinal number?

Answer 22

A number defining the position of something in a series.

Question 23

What is a cardinal number?

Answer 23

A number denoting quantity.

Question 24

What number is not a cardinal number?

Answer 24

0

Question 25

Give three examples of cardinal numbers.

Answer 25

First, second, third.

Question 26

Give three examples of cardinal numbers.

Answer 26

One, two, three.

Question 27

Give an example of when an integer could be used.

Answer 27

Used as a counter to keep track of how many times a loop statement is reapeated.

Question 28

Give an example of when a natural number could be used.

Answer 28

To identify the location of data within data structure.

Question 29

Give an example of when real numbers could be used.

Answer 29

Used by CNC machines to handle measurements that vary from millimetres to metres and must work to high degrees of accuracy.

Question 30

What is a set?

Answer 30

A collection of ordered values where each value appears only once.

Question 31

Draw the set of real numbers table out.

Answer 31

See booklet.

Question 32

What are the values is a set referred to as?

Answer 32

Elements, objects, members.

Question 33

What is it called when you define a set?

Answer 33

Set comprehension or set building.

Question 34

What does the ‘pipe’ mean? ( | )

Answer 34

Such that

Question 35

What does E mean in a set?

Answer 35

Is a member of

Question 36

What does ^ mean?

Answer 36

And

Question 37

How do you read sets?

Answer 37

The set ___ is defined in terms of x such that x is a member of the set of ___ numbers, and x is …

Question 38

Do infinite sets have cardinality?

Answer 38

No

Question 39

Why do infinite sets not have cardinality?

Answer 39

Total size of the set is not known.

Question 40

What is a countable infinite set?

Answer 40

An infinite set that can be counted, however, the end of the is never reached.

Question 41

Give an example of an infinite set.

Answer 41

Atomic half-life.

Question 42

What is the cardinality of an empty set?

Answer 42

0

Question 43

What are the symbols of an empty set?

Answer 43

See booklet.

Question 44

What is the Cartesian product?

Answer 44

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.

Question 45

What is the symbol for a subset?

Answer 45

See booklet.

Question 46

What is the symbol for a proper subset?

Answer 46

See booklet.

Question 47

What is a subset?

Answer 47

When all elements of one set are contained in another.

Question 48

What is a proper subset?

Answer 48

A subset has fewer elements than the other set.

Question 49

What is the symbol for ‘not a subset’?

Answer 49

See booklet.

Question 50

What is the symbol for ‘not a proper subset’?

Answer 50

See booklet.