We derive the fading number of a general (not necessarily Gaussian) single-input multiple-output (SIMO) fading channel with memory, where the transmitter and receiver-while fully cognizant of the probability law governing the fading process-have no access to the fading realization. It is demonstrated that the fading number is achieved by IID circularly-symmetric inputs of log squared-magnitude that is uniformly distributed over a signal-to-noise (SNR) dependent interval. The upper limit of the interval is the logarithm of the allowed transmit power, and the lower limit tends to infinity sub-logarithmically in the SNR. Among the new ingredients in the proof is a new theorem regarding input distributions that escape to infinity. Upper and lower bounds on the fading number for SIMO Gaussian fading are also presented. Those are computed explicitly for stationary m-th order auto-regressive AR(m) Gaussian fading processes.