About this book

What this book is

This is a reference book of proofs. Every page shows why one fact is true, in the shortest way a reader can follow rather than the shortest way there is. Most of them have something you can move, so the reason is visible rather than only readable.

This is not a course. There are no chapters and no questions to practise. You can read a proof on its own, or follow a link to it from the page that stated the fact.

Who made it

This book is part of Open.Textbook, an independent project by Leon Vaughan, who wrote and assembled it.

Where the content comes from

The claims about which course a proof belongs to rest on the subject content published by the Department for Education. That material is Crown copyright, and it is used here under the Open Government Licence v3.0.

The specification content, and any wording taken from a specification, belongs to the awarding bodies.

The claims in this book rest on these documents:

These sources were last checked on 2026-10-12.

No awarding body endorses this book, and the Department for Education does not supply it.

Reporting a mistake

If you find a mistake, report it as an issue on the project's GitHub page: https://github.com/leonpjvaughan/Open.Textbook/issues/new.

That route needs a free GitHub account. The project has no email address, because it does not run a mail service.

In your report, say which page you were reading, what you expected, and what you saw. That is enough to find the mistake and fix it.

Licence

This book is available under Creative Commons Attribution 4.0 International. That covers the text and figures written for this book. Material from the sources listed above keeps its own copyright and licence.