Abstract
This note gives a simple natural example of a surjective inverse limit system with empty limit. For each finite subset a of the uncountable set R, let Xx be the set of injections of a into the integers. Each Xa is countable, and for a£/3 the restriction map X0-+Xx is surjective. But the inverse limit of the Xx is empty, since an element of it would give an injection of R into the integers.
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