What kinds of sets are there in algebra?

Answer 1

There are all kinds of sets in algebra. And that may not help, but it's true. There is a whole branch of algerbra that deals with the (algebraic) manipulation of sets. And don't even think about going to look at set theory. There are several branches of that, and it may well just add confusion. Sets, which are, in general, groups of "things" that are considered and manipulated as a "whole thing" by rules of mathematics, can vary in number. Just as an infinite number of things can be considered to be part of a set, there are many, many different kinds of things that can be put into a set.

How about a "regular" set of table flatware? Subsets would be knives, salad forks, dinner forks, soup spoons and teaspoons. (Leave out all the "fancy" stuff.) How about a set of the stuff that goes on the right side of the plate in a "regular" setting as a subset of flatware? That'd be the knife and spoons. See how this works? It could take you all day to make sets of the things in your house. And the sets could be anything! Things made completely of metal, completely of wood, completely of glass (excluding ceramics). Things normally found in the kitchen could be a set, or it could be a subset of the stuff in your house. We could go on and on.

In number theory, there are some interesting problems of sets, but, again, sets can be as varied as the imagination of the person dreaming them up....

Kinds of set:

*infinite set:

-the set continues on for infinity.There may not be an infinite amount of a thing you wear, it is limited to numbers.

*finite set:

-it has finite (countable) number of elements, it has unlimited numbers.

*numerical set:

-a set having only numbers as its elements, set prime numbers (2,3,5,7,11,13,17..)

*equal set:

-two sets are equal if they have precisely the same numbers.

*null set:

-its is a set with no elements or numbers.

*equivalent set:

-sets with the same numbers of members .

*intersecting sets:

-sets with some members in common.

*subsets:

-sets contained within others are subset.