structural:expansion, stylistic:tone, structural:summarization
A field with four elements

In addition to familiar number systems such as the rationals, there are other, less immediate examples of fields. The following example is a field consisting of four elements called O, I, A, and B. The notation is chosen such that O plays the role of the additive identity element (denoted 0 in the axioms above), and I is the multiplicative identity (denoted 1 in the axioms above). The field axioms can be verified by using some more field theory, or by direct computation. For example,

This field is called a finite field or Galois field with four elements, and is denoted F or GF(4). The subset consisting of O and I (highlighted in red in the tables at the right) is also a field, known as the binary field F or GF(2).