% Group terms using parentheses.
\providecommand*{\qty}[1]{ \left( {#1} \right) }
+% Group terms using square brackets.
+\providecommand*{\sqty}[1]{ \left[ {#1} \right] }
+
% Create a set from the given elements
\providecommand*{\set}[1]{ \left\lbrace {#1} \right\rbrace }
% A pair of things.
\providecommand*{\pair}[2]{ \left( {#1}, {#2} \right) }
+
+%
+% 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
+}
+
+% The integral n-space, Z x Z x Z x ... x Z.
+\providecommand*{\Zn}[1][n]{
+ \mathbb{Z}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
+}
+
+% The rational n-space, Q x Q x Q x ... x Q.
+\providecommand*{\Qn}[1][n]{
+ \mathbb{Q}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
+}
+
+% The real n-space, R x R x R x ... x R.
+\providecommand*{\Rn}[1][n]{
+ \mathbb{R}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
+}
+
+% The complex n-space, C x C x C x ... x C.
+\providecommand*{\Cn}[1][n]{
+ \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
+}