# Constructive gem: double exponentials

In the last constructive gem we studied the exponential $2^\mathbb{N}$ and its isomorphic copies. This time we shall compute the double exponential $2^{2^\mathbb{N}}$ and even write some Haskell code. Continue reading Constructive gem: double exponentials

# Constructive gem: juggling exponentials

Constructive gems are usually not about particular results, because all constructive results can be proved classically as well, but rather about the method and the way of thinking. I demonstrate a constructive proof which can be reused in three different settings (set theory, topology, computability) because constructive mathematics has many different interpretations.

# Constructive stone: minima of sets of natural numbers

I promise I will post a constructive gem soon. This constructive stone came up as a reaction to the cardinality of finite sets stone. I show that inhabited sets of natural numbers need not have minima, constructively.

# Constructive stone: cardinality of sets

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.