User blog:Naruyoko/My Tottaly Not Broken "Ordinal Notation", Which Totally is Well-Defined and Covers All Ordinals To the Limit Ok Why Is the Title so Long

Ok.

Definition of ordinals...

...

I'm just going to skip it.

P1

1:1. The notation consists of \(t\), which then must be followed by \((\), which must then be followed by a \\), or another expression of this, then \\). For example, \(t(t)\).

1:2. \(t=0\)

1:3. \(t(r)=r+1\), where \(r\) is an expression.

The limit of this is \(t(\cdots)\), or \(\omega\).

P2

2:1. The notation consists of \(t\), which then must be followed by \((\), then an array, then \\). For example, \(t(t,t(t^2))\).

2:2. An array is either nothing, an expression, an expression, expression with superscript of an expression \(\lt t(0,1)\), a variable name with superscript of an expression \(\lt t(0,1)\), or an array followed by a \(,\), and then an array.

2:3. Array in form of \(a_1,\cdots,a_n,0\), anywhere, is equivalent to \(a_1,\cdots,a_n\).

2:4. Array in form of \(a_1,\cdots,a_n,\), anywhere, is equivalent to \(a_1,\cdots,a_n\).

2:5. \(t=0\)

2:6. \(t(r)=r+1\), where \(r\) is an expression.

2:7. \(t(t(a),r)=t(t(a,r))\), where \(a\) is an expression and \(r\) is an array.

2:8. Wait what was I doing?

Oh wow this is tttttterrible.