+% The Cartesian product of two things.
+\providecommand*{\cartprod}[2]{ {#1} \times {#2} }
+
+%
+% Product spaces
+%
+% All of the product spaces (for example, R^n) that follow default to
+% an exponent of ``n'', but that exponent can be changed by providing
+% it as an optional argument. If the exponent given is ``1'', then it
+% will be omitted entirely.
+%
+
+% The natural n-space, N x N x N x ... x N.
+\providecommand*{\Nn}[1][n]{
+ \mathbb{N}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
+}
+