The grade of an element $$\mathbf x$$ is denoted by $$\operatorname{gr}(\mathbf x)$$, and the antigrade is denoted by $$\operatorname{ag}(\mathbf x)$$. In an n-dimensional geometric algebra, it is always the case that
$$\operatorname{gr}(\mathbf x) + \operatorname{ag}(\mathbf x) = n$$ .