What ∎ means
The author is marking the proof as complete. The square usually sits at the end of the last line, often pushed to the right margin, so a reader skimming a textbook can see where one argument stops and the next text begins. It replaces QED, short for the Latin quod erat demonstrandum, "which was to be demonstrated". It marks the end, not a guarantee that the reasoning is right.
A filled ∎ and a hollow mean exactly the same thing. Which one a book shows is a choice of its designer or typesetting software.
Where did the square come from?
From magazines, via the mathematician Paul Halmos. Closing a proof with a set phrase goes back to Euclid, who ended proofs with the Greek version of "which was to be shown"; the Latin wording appears in printed Euclid translations by 1505. The square came much later: Halmos said he borrowed the end-of-article mark used in magazines, and his use in mathematics dates to around 1950. Mathematicians named it after him, and its upright block shape earned it the nickname tombstone.
Formal mathematics by default; outside it, a nerdy, mock-triumphant "done, proven".
Used to end a debate, it can come across as smug.
Part of the collection
Don't confuse it with
3
Combination ideas
3Questions people ask
3Why is it called a tombstone?
Because of its shape. The small upright block looks like a gravestone, and it marks the spot where the argument is laid to rest.
Is the hollow square different from the filled one?
No. and ∎ both mean the proof is finished; the style depends on the book or software.
What does ∎ mean at the end of a social media post?
It's a joke borrowed from maths: "and that settles it". The writer is presenting their point as proven.
More like this
14
Collections with ∎
3
How to type or find ∎
- Also called
- QED symbol · tombstone · Halmos symbol
- Search it as
- qed · halmos · black square proof · proof box · q.e.d.
- Shows up in
- Anything that takes text · its shape is whatever your font draws
∎\220ECodes and encoding1 code points
A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.