The -ag notation is a generalized form of the gag and mag functions by the googologist André Joyce. Joyce defined \(\mathrm{bag}(n) = \mathrm{mag}^n(n)\), \(\mathrm{trag}(n) = \mathrm{bag}^n(n)\), \(\mathrm{quadrag}(n) = \mathrm{trag}^n(n)\), etc., in accordance to the -illion series. -ag forms a fast iteration hierarchy with \(f_0(n) = A(n, n)\).