Finite algebra

Finite algebra is like solving puzzles using numbers and symbols. It's like playing a game where you have to figure out what the missing number or symbol is by using the rules and equations given to you.

But instead of using regular numbers like 1, 2, 3, and so on, we use a special set of numbers that are only allowed to be used in the game. These numbers are called "finite field elements."

Think of it like having a set of 5 toys to play with. You can use those toys to build different things, but you can't use any other toys that aren't in that set.

In this game, we can add, subtract, multiply, and divide the finite field elements just like regular numbers, but there are some special rules that only apply to these specific numbers.

For example, if we have two finite field elements, let's say 2 and 3, and we want to add them together, we would write it like this:

2 + 3 = ?

But instead of getting 5 as the answer, we have to use a special rule in the game which says that we always have to reduce our answer to a certain number within the set of finite field elements.

So if we're playing with the set of numbers {0, 1, 2, 3, 4} and we add 2 and 3, we would get 5 as our answer. But since 5 is not in our set of numbers, we have to reduce it until we get a number that is.

We do this by dividing the answer by the number of elements in the set (which is 5 in this case) and taking the remainder.

So 5 divided by 5 is 1 with a remainder of 0. And since 0 is in our set of numbers, our answer is 0!

So 2 + 3 in our finite algebra game is equal to 0.

This might seem a little complicated at first, but once you get the hang of the rules, it becomes like a fun puzzle to solve!