Definition:Subtraction/Field

Definition

Let $\struct {F, +, \times}$ be a field.

The operation of subtraction $a - b$ on $F$ is defined as:

$\forall a, b \in R: a - b := a + \paren {-b}$

where $-b$ is the (field) negative of $b$.

Sources

• 1973: C.R.J. Clapham: Introduction to Mathematical Analysis ... (previous) ... (next): Chapter $1$: Axioms for the Real Numbers: $2$. Fields
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): field: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): field: 1.