User:RealAngus/Angus's ordinal notation/Linear ordinal notation

This is the first part of my ordinal notation

Rules:
[0]=0

[a,...]=s([a-1,...])

[0,...,0,a,...][n]=[0,...,n,a-1,...]

Comparisons:
[0]=0

[1]=1

[2]=2

[0,1]=w

[1,1]=w+1

[0,2]=w2

[0,0,1]=w^2

[1,2,3]=(w^2)3+w2+1

[0,0,0,1]=w^3

[0,0,0,0,0,0,0,0,0,0,1]=w^10