Hello LMaD.
I am here to discuss mathematics with you....
We will discuss set-builder notation below:
Sets are merely mathematical "structures"/objects that enclose other mathematical objects.
Typical set notation is through the use of the curly-bracket characters, {}.
Sets are quite useful for modeling the properties of "concrete", real-world objects.
A sufficient example would be a young child's playpen. The playpen can contain many "toy" objects. Those "toy" objects are enclosed within the playpen. Hence, they are "elements" or "members" of the playpen.
Mathematically, we could express the playpen(And its elements) as this:
P = {Rubber Car,Brunette-Doll,Dinosaur};
"P" refers to the actual playpen set. All of the remaining names merely refer to the members of the playpen.
There is an inherent issue with the above: It assumes that all elements within the set are always toys. Well, since it is preferable to have only "child-safe" objects within a playpen, it is necessary to ensure that only permissible objects will be added into our set. The below example accomplishes this:
P = {o | T(o) = 1}
To a novice, the above may seem rather "complicated", though I assure you that the concept is actually much simpler than it appears.
"o" is the actual object that may become a member of playpen P. Function "T" accepts a object as its input and determines whether the input object is an actual toy.
If the object is a toy, 1 is the output value. If the object is not a toy, 0 is the output value.
Consequently, in this example, all objects that are toys(And consequently output 1) are enclosed within the playpen. Therefore, they are members of set P.
Mathematically, notation such as "x | condition" means in regular language that "all x values that fulfill a specific condition truthfully"
Hopefully this has provided an interesting subject to many users. |