Follow your curiosity

What discovery has been shared with you?

FACTREE gives you something interesting to discover every day — and something worth talking about together.

Start with one fact. Explore it, go deeper, then follow whichever branch catches your imagination.

Choose subjects for a surprise

Exploring any topic

Begin your discovery

Your next discovery is one click away.

Choose one or more subjects above, or leave Any Topic selected and let curiosity decide.

Mathematics

Axiomatic Set Theory and the Zermelo–Fraenkel Axioms

Quick fact

The set of all sets that do not contain themselves cannot exist—this is Russell's Paradox, which led to the creation of axiomatic set theory in the early 20th century.

Why this is interesting

You've used sets since kindergarten—putting things in groups—but did you know that without a few strict rules, sets can create paradoxes that break mathematics itself?