What a sigma-algebra is: a collection of sets closed under complement and countable union

What bloom filters do: probabilistically check set membership with no false negatives

Bloom filters: Efficient set membership testing with zero false negatives

What the Y combinator does: enables recursion in languages without named functions

The Y combinator enables recursive function definitions in lambda calculus and similar functional languages

How do Bloom filters utilize bit arrays to efficiently perform probabilistic set membership tests with minimal false positives?

Bloom filters use bit arrays to store hashed positions, allowing quick membership checks with controlled false positives

What CAP theorem states: you can have at most 2 of consistency, availability, partition tolerance

CAP theorem: Consistency, Availability, Partition Tolerance; only 2 can be fully achieved simultaneously

How does the concept of homotopy type theory (HoTT) enable the unification of homotopy theory and higher category theory in mathematical foundations?

HoTT unifies homotopy theory and higher category theory by using types as mathematical objects, enabling homotopical and categorical structures to coexist

Write the equation for sigmoid function σ(x) = 1/(1+e^-x)

σ(x) = 1 / (1 + e^-x)