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Definition

This is how to subtract one from array. It enables 3(1,0)3.

Let the identifier i.

  1. If the last number is more than zero, just subtract one from it.
  2. If the last number is zero,
  3. If the last forms "...Ax,0,...,0",
    SDAx,0,...0=SDA(x-1),i,...,i
    1. Else (which forms "Ax(n)0"),
      SDAx(n)0=SDAx-1(n)i(n-1)i(n-1)...i(n-1)i (i i's)
  1. Combinated version example:
    When identifier is 5,
    3,0(1)0,0-1=2,5(1)5,5-1=2,5(1)5,4


Comparison

SDx(1,0)x=SDx(x)x\simeq f_{\omega^{\omega^{\omega}}}(x)

SDx(1,0)(1)x\simeq f_{\omega^{\omega^{\omega}+1}}(x)

SDx(1,0)(1,0)x\simeq f_{\omega^{\omega^{\omega}*2}}(x)

SDx(1,1)x\simeq f_{\omega^{\omega^{\omega+1}}}(x)

SDx(2,0)x\simeq f_{\omega^{\omega^{\omega*2}}}(x)

SDx(1,0,0)x\simeq f_{\omega^{\omega^{\omega^2}}}(x)

So, I guess adding a next of bracket gives two more omegas. Therefore, the limit of this notation is \epsilon_0.

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