Surreal number/Simplicity

■ Surreal number/Simplicity illustrates that illustrates a case where the surreal number $x$ is not midway bwetten $X_{L}$ and $X_{R}$ (as it is for { 0 | 1 } = 1/2, { 0 | 1/2 } = 1/4, and { 1/2 | 1 } = 3/4.)

$\{2{\tfrac {1}{2}}|4{\tfrac {1}{2}}\}=3$, not ${\color {Red}3{\tfrac {1}{2}}}$ (which is the average of $2{\tfrac {1}{2}}$ and $4{\tfrac {1}{2}}$)

Instead, the simplicity rule yields:

$\{2{\tfrac {1}{2}}|4{\tfrac {1}{2}}\}=\{2|\;\}=3,$

which is the oldest number between $2{\tfrac {1}{2}}$ and $4{\tfrac {1}{2}}.$

...the rest is under construction...💧