Paraconsistent second order arithmetic Z^#_2 based on the paraconsistent logic LP^# with infinite hierarchy levels of contradiction. Berrys and Richards inconsistent numbers within Z^#_2

In this paper paraconsistent second order arithmetic Z#2 with unrestricted comprehension scheme is proposed. We outline the development of certain portions of paraconsistent mathematics within paraconsistent second order arithmetic Z#2.In particular we defined infinite hierarchy Berrys and Richards inconsistent numbers as elements of the paraconsistent field R^#.