Edgeworth's conjecture that as the number of traders in an exchange economy increases the core approaches the set of competitive equilibria has been formalized both as a theorem about a sequence of finite economies, and as a theorem about an economy having an infinite number of agents. This paper, using nonstandard analysis, provides a synthesis of these two approaches. It is shown that the core and the set of competitive equilibria are equivalent within a non-standard exchange economy. This theorem implies a asymptotic theorem concerning the core and competitive equilibria of sequences of finite economies.