The order of elements in the set does not matter. We could just as well write S = {N ader, Buchanan, Gore, Bush}. In general, two sets are the same if and only if they have exactly the same members
Step-by-step explanation:
Defn: A set is a collection of individuated or distinct objects or things. A member of a set
is called an element.
1.1 Finite sets
Defn A finite set has a finite number of elements. Finite sets are represented as follows:
S = {Gore, Bush, Buchanan, Nader}
• “S” is the name of the set. This is arbitrary. We could use any letter or symbol as the
name. There are some conventions here, however. Sets are usually named with capital
letters, and one usually picks a letter that has some mnemonic value. Here, “S” for
“set,” but we might have used, say, “C” for “candidates.”
• “Gore,” “Bush,” etc. are elements of S. They are enclosed by the brackets “{” and
“}” which are used to denote a set. The order of elements in the set does not matter.
We could just as well write S = {Nader, Buchanan, Gore, Bush}. In general, two sets
are the same if and only if they have exactly the same members.
• “Gore ∈ S” reads “Gore is a member of the set S.” “∈” means “is a member of” or “is
in”.
• The members of sets must all be distinct objects. For example A = {Bush, Gore,
Bush} is not a set if both Bushs refer to the same object.
Note, however, that you may encounter sets such as S = {cooperate, cooperate}. Here
it would be implicitly understood that the elements refer to (in this example) a strategy
for player 1 (the first “cooperate”) and a strategy for player 2 (the second one).
• The elements of sets need not be numbers. They can be practically any things that can
Answers & Comments
Answer:
The order of elements in the set does not matter. We could just as well write S = {N ader, Buchanan, Gore, Bush}. In general, two sets are the same if and only if they have exactly the same members
Step-by-step explanation:
Defn: A set is a collection of individuated or distinct objects or things. A member of a set
is called an element.
1.1 Finite sets
Defn A finite set has a finite number of elements. Finite sets are represented as follows:
S = {Gore, Bush, Buchanan, Nader}
• “S” is the name of the set. This is arbitrary. We could use any letter or symbol as the
name. There are some conventions here, however. Sets are usually named with capital
letters, and one usually picks a letter that has some mnemonic value. Here, “S” for
“set,” but we might have used, say, “C” for “candidates.”
• “Gore,” “Bush,” etc. are elements of S. They are enclosed by the brackets “{” and
“}” which are used to denote a set. The order of elements in the set does not matter.
We could just as well write S = {Nader, Buchanan, Gore, Bush}. In general, two sets
are the same if and only if they have exactly the same members.
• “Gore ∈ S” reads “Gore is a member of the set S.” “∈” means “is a member of” or “is
in”.
• The members of sets must all be distinct objects. For example A = {Bush, Gore,
Bush} is not a set if both Bushs refer to the same object.
Note, however, that you may encounter sets such as S = {cooperate, cooperate}. Here
it would be implicitly understood that the elements refer to (in this example) a strategy
for player 1 (the first “cooperate”) and a strategy for player 2 (the second one).
• The elements of sets need not be numbers. They can be practically any things that can
Hope its help