Cardinality of sets in constructive mathematics is not as well behaved as in classical mathematics. Cardinalities of finite sets are *not* natural numbers, and cardinalities are *not* linearly ordered.

# Category Archives: Gems and stones

# Constructive stone: finite sets

Just like in real life, constructive stones are easier to find than constructive gems, so let me start the series with a stone about constructive finite sets.

Two girl one cup

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# Constructive gems and stones

In various mathematical forums, mostly those of a logical flavor, I regularly see people asking basic questions about constructive mathematics. I also see misconceptions about constructive mathematics. I shall make a series of posts, *Constructive Gems and Stone*s, which will answer basic questions about constructive mathematics, and will hopefully help fix wrong ideas about constructive mathematics.

A constructive *gem* is something nice about constructive mathematics that makes you want to know more about it. In contrast, a constructive *stone* is a complication in constructive mathematics which does not exist in the classical counterpart.

Here we go! The first one is about finite sets.