Sets + Numbers (W1+W2)

Question 1

What is a subset

Answer 1

A set thats included in another set

a Set A is included in a Set B IFF anything that is a member of A is a member of B

Question 2

what is a Power Set

Answer 2

the set of all subsets of a set

P{A} = {X:X C A}

Question 3

What is an element

Answer 3

an element is a member of a set

Question 4

what is the definition of Countably Infinite

Answer 4

1. A set is countably infinite if its elements can be put into a 1-1 correspondence with natural numbers (or a proper sub-set of its)
2. the set may contain an infinite amount of elements but can be ‘counted’/’enumerated’ in a systematic way

Question 5

provide an example of a countably infinite set

Answer 5

1. the Set of all natural numbers

each natural number can be uniquely matched with itself

Question 6

what is a finite set

Answer 6

1. A set is finite if it contains a specific number of elements

Question 7

provide an example of a finite set

Answer 7

1. the set of all natural numbers less than 5 {1,2,3,4}

Question 8

what is the definition of an uncountably infinite set

why?

Answer 8

1. A set is uncountably infinite if its elements cannot be put into 1-1 correspondence with the natural numbers
2. there are more elements in the set than there are natural numbers

Question 9

provide an example of an uncountably infinite set

Answer 9

1. the set of real numbers - It includes both ‘rational’ + ‘irrational’ numbers

Question 10

what is a rational number

provide an example

Answer 10

A rational number is a number that can be expressed as A/B where A/B are integers and B is not 0

345/647

Question 11

what is a real number

provide an example

Answer 11

A real number is any number that can be represented in decimal notation where there can be an infinite sequence after the decimal point

12.147

Question 12

What is an integer

provide an example

Answer 12

An integer are positive and negative whole numbers

-3,-2,-1,0,1,2,3

Question 13

what is a natural number

provide an example

Answer 13

whole positive numbers including 0

0,1,2,3

Question 14

what is an irrational number

provide an example

Answer 14

An irrational number cannot be expressed as a finite decimal, or as a decimal with a repeating pattern

Pi - 3.14159265

Question 15

what is the relation between Real numbers, rational numbers and irrational numbers

Answer 15

Real numbers include irrational numbers and rational numbers

Question 16

what is a Proper Subset

Answer 16

a Set A is a proper subset of B IFF A is a subset of B but not identical to B

every member of A is a member of B but some members of B are not members of A

Question 17

What is the definition of equinumerosity

Answer 17

two sets are equinumerous IFF we can put them into a 1-1 correspondence