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Two approximations to the Shannon capacity of a maximal-ratio combining (MRC) diversity system are proposed in terms of the diversity factor (DF). Asymptotic analysis shows that the approximations are identical to the true capacity in the low-SNR regime and have the same slope but different power offsets in the high-SNR regime. For Rayleigh-fading environments, the power offset differences are derived and shown to be considerably small quantities. Thus, the DF can be considered as an effective measure of the asymptotic capacity improvement offered by MRC diversity reception in Rayleigh fading channels.