1 Sets, Relations, and Arguments: 1.1 Sets Flashcards
What is a set?
A set is collection of objects
What may the objects of a set be?
Concrete objects, such as persons and planets;
Non-concret objects, such as numbers or other sets
What are the objects in the collection called?
Elements of that set
When are sets identitcal?
If and only if they have the same elements
How would one write ‘a is an element of the set S’ symbolically?
a ∈ S
If a is an element of S, what can one also say?
That a is in S; or that S contains a
How many sets contain no elements? How is this represented?
There is exactly one set that contains no elements, namely, the empty set ∅
How can one write down the names of the elements, or other designations, of the elements?
By enclosing this list in curly brackets. For example, the set of London and Munich would be written as such: {London, Munich}
What can be said about the set {London, Munich} and the set {Munich, London}?
That they are identical, for they have the same elements.
{London, Munich} = {Munich, London}
If a set is specified by including names for the elements in curly brackets, what does not matter?
The order of the names
What are the sets {the captial of England, Munich} and {London, Munich}
Still the same set, becasue ‘the capital of England’ is just another way to designate London
What does adding another name for something to a set which already contains said thing not do?
It does not add a further element
How can one designate the elements of a set which is impractical to list semi-formally, such as ‘the set of all animals with a heart’?
{x : x is an animal with a heart
