- #1
zrek
- 115
- 0
Please help me to define correctly, in the language of mathematics, the configuration of sets shown on the picture.
I'd like to define the following rules:
U is a set with infinite members.
L is a list or set of properties. Every property (Ls1, Ls2 ... ) have a value ( 0,1,2,...P )
Every member of U is defined by its unique property list. Every member is paired with one and only one value from each of the Ls1,Ls2... properties.
The U contains i+1 subsets.
F is a list of functions, or it is the set of subsets of U.
Every subset of U is paired with a function in F, except one, which contains all of the members which are not in any subsets defined by F.
The subsets of U are determined the following way:
An Xk member of U is in subset Fj, ( 1<=j<=i ) if the function Fj outputs "true" after processing the Ls1, Ls2 ... values of Xk.
For example:
Properties of X0 are:
Ls1: 3
Ls2: 2
Ls3: 5
...
Since only the function F1 returns "true" for this input, the X0 is solely in the F1 subset of U.
I have difficulties even to correctly define the L set and the members of U.
Would you please help me to start somehow?
Thank you in advance.
Homework Statement
I'd like to define the following rules:
U is a set with infinite members.
L is a list or set of properties. Every property (Ls1, Ls2 ... ) have a value ( 0,1,2,...P )
Every member of U is defined by its unique property list. Every member is paired with one and only one value from each of the Ls1,Ls2... properties.
The U contains i+1 subsets.
F is a list of functions, or it is the set of subsets of U.
Every subset of U is paired with a function in F, except one, which contains all of the members which are not in any subsets defined by F.
The subsets of U are determined the following way:
An Xk member of U is in subset Fj, ( 1<=j<=i ) if the function Fj outputs "true" after processing the Ls1, Ls2 ... values of Xk.
For example:
Properties of X0 are:
Ls1: 3
Ls2: 2
Ls3: 5
...
Since only the function F1 returns "true" for this input, the X0 is solely in the F1 subset of U.
The Attempt at a Solution
I have difficulties even to correctly define the L set and the members of U.
Would you please help me to start somehow?
Thank you in advance.