Real equivalent of the surreal number {0.5|} I've been reading up on Surreal numbers, but have some questions. Some equivalent real and surreal numbers. 2.5 = {2|3} = {{{0|}|}|{{{0|}|}|}} = {{{{{|}}|{}}|{}}|{{{{{|}}|{}}|{}}|{}}} 0 = {-1|1} = {-2|1} = {-2,-1|1} = {{|0}|{0|}} = {{|{|0}},{|0}|{0|}} = {{{}|{{|}}}|{{{|}}|{}}} -3/8 = {-0.5|-0.25} = {{-1|0}|{{-1|0}|0}} {{{{}|{{|}}}|{{{}|{{|}}}|{{|}}}}|{{{}|{{|}}}|{{|}}}} What about the real number for {0.5|}?

In the surreal numbers, $$\\{0.5|\\}=1=\\{0|\\}=\\{\\{|\\}|\\}.$$

In general, if $a$ is real and $a\ge 0$, $$\\{a\mid\\}=\\{\lfloor a\rfloor\mid\\}=\lfloor a \rfloor+1,$$ where $\lfloor a \rfloor$ is the largest integer less than or equal to $a$. If $a<0$, $$\\{a\mid\\}=\\{\mid\\}=0.$$