So far we have been discussing sets. These are extremely simple objects, essentially mathematical “bags of stuff.” Without any added structure, their usefulness is very limited. A set with no added st...So far we have been discussing sets. These are extremely simple objects, essentially mathematical “bags of stuff.” Without any added structure, their usefulness is very limited. A set with no added structure will not help us, say, solve a linear equation. What will help us with such things are objects such as groups, rings, fields, and vector spaces. These are sets equipped with binary operations which allow us to combine set elements in various ways.
The product of two whole numbers is the same regardless of the order of the factors. If three whole numbers are multiplied, the product will be the same if the first two are multiplied first and then ...The product of two whole numbers is the same regardless of the order of the factors. If three whole numbers are multiplied, the product will be the same if the first two are multiplied first and then that product is multiplied by the third, or if the second two are multiplied first and that product is multiplied by the first. (a first number ⋅ a second number)⋅a third number=a first number⋅(a second number ⋅ a third number)
