It is not inversion but a relative clause: the infinite number of ways ( that ) there are
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GPYIt is not inversion but a relative clause:the infinite number of ways (that) there areThank you for the reply.
GPYJack built the housethe house (that) Jack builtthere are an infinite number of waysthe infinite number of ways (that) there areThank you for the reply.
AnonymousIs "there" a dummy or locative one in the infinite number of ways (that) there are?It's a dummy "there", used to state the existence of something in the expression "there are ...".