Editing Surreal number (section)

===Multiplication===
Multiplication can be defined recursively as well, beginning from the special cases involving 0, the [[multiplicative identity]] 1, and its additive inverse −1:
<math display=block>\begin{align}
xy & = \{ X_L \mid X_R \} \{ Y_L \mid Y_R \} \\
   & = \left\{ X_L y + x Y_L - X_L Y_L, X_R y + x Y_R - X_R Y_R \mid X_L y + x Y_R - X_L Y_R, x Y_L + X_R y - X_R Y_L \right\} \\
\end{align}</math>
The formula contains arithmetic expressions involving the operands and their left and right sets, such as the expression <math display=inline>X_R y + x Y_R - X_R Y_R</math> that appears in the left set of the product of {{mvar|x}} and {{mvar|y}}. This is understood as <math display=inline>\left\{ x' y + x y' - x' y' : x' \in X_R,~ y' \in Y_R \right\}</math>, the set of numbers generated by picking all possible combinations of members of <math display=inline>X_R</math> and <math display=inline>Y_R</math>, and substituting them into the expression.

For example, to show that the square of {{sfrac|1|2}} is {{sfrac|1|4}}:
:{{math|1={{sfrac|1|2}} ⋅ {{sfrac|1|2}} = {{mset| 0 {{!}} 1 }} ⋅ {{mset| 0 {{!}} 1 }} = {{mset| 0 {{!}} {{sfrac|1|2}} }} = {{sfrac|1|4}}}}.