On Dividing by Two in Constructive Mathematics
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congconstructivemathematicstimesaxiombernsteincannotchoice
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A classic result due to Bernstein states that in set theory with classical logic, but without the axiom of choice, for all sets $X$ and $Y$, if $X \times 2 \cong Y \times 2$ then also $X \cong Y$. We show that this cannot be done in constructive mathematics by giving some examples of toposes where it fails.
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