User blog comment:Edwin Shade/Surreals and the Nature of Number/@comment-11227630-20171215001641

{{|}|{|}} is not a surreal number, because the {|} in the left is equal to the {|} in the right.

$$\omega^\pi=\{\omega^{(11)_2},\omega^{(11.001)_2},\omega^{(11.001001)_2},\omega^{(11.00100100001)_2},\omega^{(11.001001000011)_2},\cdots|\omega^{(11.1)_2},\omega^{(11.01)_2},\omega^{(11.0011)_2},\omega^{(11.00101)_2},\omega^{(11.0010011)_2},\cdots\}$$. Its elements can be achieved by multiplication, e.g. $$\omega^{(11.001)_2}=\omega^2\times\omega\times\omega^{\frac{1}{8}}$$, where $$\omega^{\frac{1}{2^n}}$$ can be achieved by nested square root of $$\omega$$.