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FRE 6083 – Quantitative Methods in Finance  Copyright F. Novomestky 2007
Set Theory Review
Definitions
Set Operations
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FRE 6083 – Quantitative Methods in Finance  Copyright F. Novomestky 2007
Set Theory  Definitions
Set = a collection of objects
Symbols for sets
É
Upper case block letters A, B, C, E,F, M, S
É
Upper case italic letters
A, B, C, E, F, M, S
Examples
É
S
1
= {heads, tails}
É
S
2
= {1, 2, 3, 4}
É
S
3
= {car, apple, pencil}
Set B is a subset of A = every element of B is an
element of A. This is written as B
⊂
A.
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FRE 6083 – Quantitative Methods in Finance  Copyright F. Novomestky 2007
Set Theory  Definitions
We consider sets (actually subsets) whose
elements are taken from a largest set called a
universe or space
S
.
Examples of Spaces
É
Role a die = {f
1
, f
2
, f
3
, f
4
, f
5
, f
6
}
É
Stocks traded on NYSE
É
Publicly traded mutual funds
Specification
É
Enumeration: {f
1
, f
2
, f
3
, f
4
, f
5
, f
6
}
É
By property : {n  n is a positive integer}
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FRE 6083 – Quantitative Methods in Finance  Copyright F. Novomestky 2007
Set Theory  Definitions
Sets are represented by uppercase letters
If x is an element of A, then we write x
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 Spring '11
 Neveskyi
 Set Theory, Naive set theory, Set Operations

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