User blog:Primussupremus/Array notation from my website endless possiblities part 2.

This is part 2: I will be starting at {K:↑(ω+1)(X)} then moving on from there.

{K:↑(ω+1)(X)} = {K:↑(ω)(X)} recursed ({K:↑(ω)(X)}-1) times.

{K:↑(ω2)(X)} = {K:↑(ω+ω)(X)}= {K:↑(ω+X)(X)} = {K:↑(ω+X-1)(X)} recursed ({K:↑(ω+X)(X)}-1) times.

{K:↑(ω3)(X)}= {K:↑(ω2+x)(X)} = {K:↑(ω2+X-1)(X)} recursed ({K:↑(ω2+X-1)(X)}-1)times.

{K:↑(ω^2)(X)}= {K:↑(ω*ω)(X)}= {K:↑(ω*X)(X)} = {K:↑(ω*X-1)(X)} recursed ({K:↑(ω*X-1)(X)}-1) times.

{K:↑(ω^ω)(X)} = {K:↑(ω^X)(X)}= {K:↑(ω^X-1)(X)} recursed ({K:↑(ω^X-1)(X)}-1)times.

{K:↑(ω^ω+(1))(X)} = {K:↑(ω^ω)(X)} recursed ({K:↑(ω^ω)(X)}-1) times.

{K:↑(ω^ω+(ω))(X)} = {K:↑(ω^ω+(X))(X)} = {K:↑(ω^ω+(X-1))(X)} recursed ({K:↑(ω^ω+(ω))(X-1)}-1) times.

{K:↑(ω^ω+(ω+1))(X)} = {K:↑(ω^ω+(ω))(X)} recursed ({K:↑(ω^ω+(ω))(X)}-1)times.

{K:↑(ω^ω+(ω2))(X)} = {K:↑(ω^ω+(ω+ω))(X)} = {K:↑(ω^ω+(ω+X))(X)}

= {K:↑(ω^ω+(ω+X-1))(X)} recursed ({K:↑(ω^ω+(ω+X-1))(X)}-1) times.

{K:↑(ω^ω+(ω^2))(X)} = {K:↑(ω^ω+(ω*ω))(X)} = {K:↑(ω^ω+(ω*X))(X)}

= {K:↑(ω^ω+(ω*X-1))(X)} recursed ({K:↑(ω^ω+(ω*X-1))(X)}-1) times.

{K:↑((ω^ω*(2))(X)}= {K:↑(ω^ω+(ω^ω))(X)} = {K:↑(ω^ω+(ω+X))(X)}

= {K:↑(ω^ω+(ω+X-1))(X)} recursed ({K:↑(ω^ω+(ω+X-1))(X)}-1) times.

{K:↑(ω^(ω+1))(X)} = {K:↑(ω^ω*ω))(X)} = {K:↑(ω^ω*X))(X)}

= {K:↑(ω^ω*X-1))(X)} recursed ({K:↑(ω^ω*X-1))(X)}-1) times.

{K:↑((ω^(ω2))(X)} = {K:↑((ω^(ω+ω))(X)} = {K:↑((ω^(ω+X))(X)}

= {K:↑((ω^(ω+X-1))(X)} recursed ({K:↑((ω^(ω+X-1))(X)}-1) times.

{K:↑((ω^(ω^2))(X)} = {K:↑((ω^(ω*ω))(X)} = {K:↑((ω^(ω*X))(X)}

= {K:↑((ω^(ω*X-1))(X)} recursed ({K:↑((ω^(ω*X-1))(X)}-1) times.

{K:↑((ω^(ω^2)+1)(X)} = {K:↑((ω^(ω^2))(X)} recursed ({K:↑((ω^(ω^2))(X)}-1) times.

You probably get the picture, the higher the ordinal the greater the strength of the array.