plz explain "universe of discourse"

Question

anonymous · Answer

universe or domain of discourse is the set of ranges that variables or entities can be. such as real numbers or natural numbers.

turingtest · Answer

We have rules, for instance, to keep the universe of discourse in algebra as only having to do with numbers. 
Peano's axiom "the successor of each number is a number" ensures that we don't get bananas, or artistic sentiments, instead of numbers as we move down the number line.

turingtest · Answer

Sometimes in mathematics we don't need the universe of discourse to be restricted to numbers, which surprises many people at first. 

For instance in set theory I can ask you about the elements in the set of all coffee cups in your house. I may ask you how many elements are in the set (which would give a numerical answer) or I may ask you to break them up into subsets (i.e. split up the white ones from the colored ones into different sets). Then our universe of discourse has innately nothing to do with numbers, at least for that moment.