User:Username5243/Introduction and analysis of UNAN p3

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Delta stage
This stage introduces the backslash, a new high-level separator. Backslashes diagonalize over / superscripts.

XXXI: introducing the backslash
As I said above, backslahes diagonalize / superscript, in a very similar way to how / diagonalizes over subscripts. The {0\x} separator approximately corresponds to /x, and the limit of page 2 is the {0\0\1} separator, which diagonalizes {0\x}.

I'm gonna give some comparisons of separators in / and \ form, to give you an idea of how they work.


 * {0/1} = {0\1}
 * {1/1} = {1\1}
 * {0{0{0/1}1}1/1} = {0{0{0/1}1}1\1} = {0{0{0{0\1}1}1}1\1}
 * {0{0/1}1/1} = {0{0/1}1\1} = {0{0{0\1}1}1\1}
 * {0{0/1}0{0/1}1/1} = {0{0{0\1}1|0{0{0\1}1}1\1}
 * {0{1/1}1/1} = {0{1{0\1}1}1\1}
 * {0{0{0/1}1/1}1/1} = {0{0{0{0\1}1}1{0\1}1}1\1}
 * {0/2} = {0/1\1} = {0{0\1}1\1}
 * {0{0/2}1/2} = {0{0{0\1}2}1{0\1}1\1}
 * {0/3} = {0{0\1}2\1}
 * {0/0,1} = {0{0\1}0,1\1}
 * {0/0/1} = {0{0\1}0{0\1}1\1}
 * {0{1}/1} = {0{1\1}1\1}
 * {0{0/1}/1} = {0{0{0\1}1\1}1\1}
 * {0//1} = {0\2}
 * {0/1//1} = {0{0\1}1\2}
 * {0//2} = {0{0\2}1\2}
 * {0//0//1} = {0{0\2}0{0\2}1\2}
 * {0{1}//1} = {0{1\2}1\2}
 * {0///1} = {0\3}
 * {0/x1} = {0\x}

And with that done, let's continue to higher ordinals.

So the limit of linear \ arrays is \(\psi(M(\omega,0))\).