What is the formula for creating a set of paired elements?

[necro_ignis]

Hi all,

I'm trying to express a given requirement in a software system. I'm used to UML and UseCase specification, but I thought I would attempt to learn Zed Specification (which is based off logic, set theory., etc... so those topics too!)

Given two sets of data
e.g. in Zed notation

[X] ::= a|b|c|d
[Y]::= 1|2|3|4

or in Set Theory

X = {a,b,c,d}
Y = {1,2,3,4}

In set notation I am having difficulty trying to write down the formula for specifying a set containing a list of pairs made from X and Y. Note: Not a Cartesian Product.
So I'm looking for a Set definition for something like this:

MysterySet = {(a,1),(b,2),(c,3),(d,4)}
or a further example,
Material = {(chair,wood),(table,metal),(cup,clay)}

This is basically an analogy for a key-value pair.

Thanks very much.

 

[Hurkyl]

I can't decipher just what it is you are trying to do...

 

[necro_ignis]

I can't decipher just what it is you are trying to do...

Hi

I'm just trying to write a set definition for a set containing a list of paired values. Where each paired value is a single member of that set.

For example the set of all married couples Married = {(bob,jane),(fred,susan),(mike,sarah)} will have been built from the two sets: female={jane,susan,sarah} and male={bob,fred,mike}

So in a set definition how do I say something like:

each element in the set "Married" is a paired value from an enumerated one-to-one mapping between an element in the set male to the set female.

Hope that help! I could do this is a second programmatically but I have become extremely interested in modeling using set theory and logic, although it's something I've only just strated learning.

Thanks

 

[necro_ignis]

After having done further research, it looks like a set of key-valued pairs might be (might be, being this is what I have thought up myself) represented as the set of all bijections as denoted X$$\leftrightarrow$$Y.

So would I be right in saying (this is so sketchy and grasping at straws)
If I have a dom X = {1,2,3} and ran Y = {a,b,c} then a set S = {f:X$$\leftrightarrow$$Y} would infact look like S={(a,1),(b,2),(c,3)}

P.S. Still getting used to the Latex function on this forum

Thanks