Infinity Fusing Notation

Infinity Fusing Notation is a notation by User:RomaronzoTHEThingy. Sadly, it can't have a similar structure to the Veblen function and you'll see why and what I mean.

$$\wr_{\beta}(\alpha) = \wr(\alpha,{\beta}) = \alpha_{\beta}$$

$$\wr(\alpha,\beta,0) nests \wr(\alpha,\alpha) \beta times$$

continue...

$$\wr(\alpha,\beta,\gamma+1) nests \wr(\alpha,\alpha,\gamma) \beta times$$

Next entry is $$\wr(\alpha,\beta,0,0)$$.

$$\wr(\beta a \alpha) = \wr(\alpha,\alpha,\alpha,\cdots,\alpha,\alpha,\alpha) \beta times$$

etc.

$$\wr(\alpha aa \beta) = \wr(\alpha a \alpha a \alpha a \cdots a \alpha a \alpha a \alpha) \beta times$$

etc.

$$\wr(\alpha Z \beta) = \wr(\alpha aaa \cdots aaa \alpha) \beta times$$