If the order (or size) of the set is p, we can call the elements of the set, 0, 1, 2, … p – 1. These numbers are what we call the elements of the set, not necessarily the traditional numbers 0, 1, 2, 3, etc. They behave in many ways like traditional numbers, but have some differences in how we add, subtract, multiply, and so forth.
In math notation the finite field set looks like this:
Fp = {0, 1, 2, ... p–1}
What’s in the finite field set are the elements. Fp is a specific finite field called “field of p" or “field of 29” or whatever the size of it is (again, the size is what mathematicians call order). The numbers between the {}s represent what elements are in the field. We name the elements 0, 1, 2, etc. because these names are convenient for our purposes.
A finite field of order 11 looks like this:
F11 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A finite field of order 17 looks like this:
F17= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
A finite field of order 983 looks like this:
F983= {0, 1, 2, ... 982}
Notice the order of the field is always 1 more than the largest element. You might have noticed that the field has a prime order every time. For a variety of reasons that will become clear later, it turns out that fields must have an order that is a power of a prime, and that the finite fields whose order is prime are the ones we’re interested in.
If the order (or size) of the set is p, we can call the elements of the set, 0, 1, 2, … p – 1. These numbers are what we call the elements of the set, not necessarily the traditional numbers 0, 1, 2, 3, etc. They behave in many ways like traditional numbers, but have some differences in how we add, subtract, multiply, and so forth.
In math notation the finite field set looks like this:
Fp = {0, 1, 2, ... p–1}
What’s in the finite field set are the elements. Fp is a specific finite field called “field of p" or “field of 29” or whatever the size of it is (again, the size is what mathematicians call order). The numbers between the {}s represent what elements are in the field. We name the elements 0, 1, 2, etc. because these names are convenient for our purposes.
A finite field of order 11 looks like this: F11 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A finite field of order 17 looks like this: F17= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
A finite field of order 983 looks like this: F983= {0, 1, 2, ... 982}
Notice the order of the field is always 1 more than the largest element. You might have noticed that the field has a prime order every time. For a variety of reasons that will become clear later, it turns out that fields must have an order that is a power of a prime, and that the finite fields whose order is prime are the ones we’re interested in.