Field (mathematics)

In mathematics, a field is a certain kind of algebraic structure. In a field, one can add (${\displaystyle x+y}$), subtract (${\displaystyle x-y}$), multiply (${\displaystyle x\cdot y}$) and divide (${\displaystyle x/y}$) two numbers (with division only possible if ${\displaystyle y}$ is non-zero). A field is a special ring in which division is possible. Both the set of rational numbers and the set of real numbers are examples of fields. The set of integers, ${\displaystyle \mathbb {Z} }$, is not a field, because the result of a division is not always an integer. One can also use the symbol ${\displaystyle \mathbb {F} }$ as a variable for a field.^[1]

1. ↑ "Greek/Hebrew/Latin-based Symbols in Mathematics". Math Vault. 2020-03-20. Retrieved 2020-10-07.