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

The Construction of the Real Numbers via Dedekind Cuts

Quick fact

A Dedekind cut is a way to 'fill the gaps' in the rationals by dividing them into two infinite sets—every rational is either in the 'left' set or the 'right' set, and the cut itself represents a real number.

Why this is interesting

You've used numbers like √2 and π, but have you ever wondered what they really are? The rational numbers have gaps, so how can we fill them to create the continuous number line?