User:Ascii/Definition:Monomial
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Definition
In elementary mathematics, a monomial is a product of:
- a number $a$ (usually from the standard number fields: $\Q$, $\R$, $\C$)
and
- a finite number of variables $x_0, \ldots, x_n$ each with respective exponents $i_0, \ldots, i_n$ from $\N_{>0}$
resulting in an expression of the form:
- $a x_0^{i_0} \ldots x_n^{i_n}$
Coefficient
In the monomial:
- $a x_0^{i_0} \ldots x_n^{i_n}$
$a$ is the coefficient.
Variable
Degree
Examples
Example 1: $2x$
$2x$ is a monomial where:
- $2$ is the coefficient
Example 2: $(7.4 - 3.12i)x^{13}yz^{7}$
$(7.4 - 3.12i)x^{13}yz^{7}$ is a monomial where:
- Coefficient: $7.4 - 3.12i$
- Variables: $x$, $y$, $z$
- Total degree: $21$ such that:
- $x$ has degree $13$
- $y$ has degree $1$
- $z$ has degree $7$