#Contents# * table of contents {:toc} ## Definition ## Given an [[algebraic limit field]] $F$, a __algebraic limit geometric algebra__ is a $F$-[[geometric algebra]] $A$ such that the limits preserve the [[algebraic limit theorem|ring structure]] and the grade projection operation: $$\prod_{f:F \to A} \prod_{n:\mathbb{N}} \langle \lim_{x \to c} f(x) \rangle_n = \lim_{x \to c} \langle f(x) \rangle_n$$ ## See also ## * [[algebraic limit field]] * [[algebraic limit vector space]] * [[algebraic limit Clifford algebra]] * [[directional derivative]] * [[geometric derivative]]