Examples
The monomial order implies an order on the individual indeterminates. One can simplify the classification of monomial orders by assuming that the indeterminates are named x1, x2, x3, ... in decreasing order for the monomial order considered, so that always x1 > x2 > x3 > …. (If there should be infinitely many indeterminates, this convention is incompatible with the condition of being a well ordering, and one would be forced to use the opposite ordering; however the case of polynomials in infinitely many variables is rarely considered.) In the example below we shall use x instead of x1, y instead of x2, and z instead of x3. With this convention there are still many examples of different monomial orders.
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