What is a symbolic rule?

Mathematics is a very powerful symbolic language.

Here we use a variety of symbols.

Here use english letters for an indefinite numbers. Not sufficient , so we use greek letters.

x, y,z stands as an unkown value for the time being. But after solving an equation x, y,z has helped us to know a value hitherto not known.

0 to 9 are,as digits , mere symbols but they are numbers as well. You can represent a counting,rational,irrational real or imaginary numbers through them.. They are capable of giving us a sense of nothingness of the world to an infinite  vastness of the universe. They can  not only measure mere objective things but also value your  abstract and imaginary ideas.

There are symbols of relation to indicate less than, greater than  or equal to (<,> and =).

A symbolic rule can indicate how a set is built :  X is a set of all  numbers between 10 to 25 represented like {: 10<x<25}

A symbolic rule  can reprsent a relation or function:

f(x)=x^2+y^2-10^2 and f(x)=0 reprents a cicle.

A sumbolic rule like: d/dx{x^n} tells us to find the first derrivative in caculus.

And there are more and very much more. Please click any search engine you get a lot.