I agree that your '@' (tetration) is one layer of 'meta' below Knuth arrows. Tetration delves past exponentiation into hyper-operations, whereas the Knuth arro

I agree that your '@' (tetration) is one layer of 'meta' below Knuth arrows. Tetration delves past exponentiation into hyper-operations, whereas the Knuth arrow generalizes them. It is just a special case that x↑↑2=x@2.