Mathematicians write QED in a proof to indicate that the proof is complete and the statement has been proven.
For a detailed answer, read below
Mathematicians write QED (sometimes written as Qed, Q.E.D. or q.e.d.) at the end of a proof to signal that the proof has been completed. QED is an abbreviation for the Latin phrase “quod erat demonstrandum,” which means “that which was to be demonstrated.” In other words, it is a way of saying “I have shown what I set out to prove.”
The use of QED dates back to ancient Greece. The mathematician Euclid used the phrase to mark the end of his proofs in “Elements,” his influential book on geometry. The practice has persisted ever since, becoming a universal symbol of mathematical proof.
Famous mathematician Paul Halmos once described the significance of QED in a quote: “The most important part of a proof is often recognising what needs to be proved, and the main message of QED is that the work is done, the rest is commentary.”
Interestingly, some mathematicians prefer to use alternatives such as “End of Proof,” “Box,” or even symbolic representations like the tombstone ◻︎ to signify the end of a proof instead of QED.
In summary, QED is a universal symbol used in mathematics to signal the completion of a proof. Its roots date back to ancient Greece, and it remains an important and recognizable part of mathematical notation today.
| Symbol | Meaning |
|---|---|
| QED | quod erat demonstrandum |
| Qed | quod erat demonstrandum |
| q.e.d. | quod erat demonstrandum |
| ◻︎ | end of proof |
| End of Proof | end of proof |
| Box | end of proof |
See additional response choices
Literally it states "what was to be shown". Traditionally, the abbreviation is placed at the end of mathematical proofs and philosophical arguments in print publications, to indicate that the proof or the argument is complete.
QED is an abbreviation of the Latin words "Quod Erat Demonstrandum" which loosely translated means "that which was to be demonstrated". It is usually placed at the end of a mathematical proof to indicate that the proof is complete.
Q.E.D. QED is an abbreviation of the Latin words "Quod Erat Demonstrandum" which loosely translated means "that which was to be demonstrated". It is usually placed at the end of a mathematical proof to indicate that the proof is complete.
"Q.E.D." (sometimes written "QED") is an abbreviation for the Latin phrase "quod erat demonstrandum" ("that which was to be demonstrated"), a notation which is often placed at the end of a mathematical proof to indicate its completion.
‘QED’ is not there as filler.
‘QED’ is there to announce the reader that the argument has been laid out in full. If the reader was following the proof, then he or she knows that now the proof is over.
This also serves a practical purpose: sometimes, the reader needs a visual cue where a proof ends. Consider, for example, the following extract:
We have two proofs here. But did you notice that there are two sentences roughly in the middle that do not pertain to any of the two proofs?
You probably did, but only because of the [math]\square[/math] symbol (signifying ‘QED’ — roughly translating to ‘as was required to be shown’) after the sentence ‘The result follows’. Note that ‘The result follows’ was sufficient to show that the proof is finished — indeed, it roughly means the same thing as ‘QED’ — but the extra [math]\square[/math] immediately after it aids the eye that, at that particular place, the proof is over.
So the ‘QED’ at the end of a proof, or whatever symbol is used to den…
In this video, you may find the answer to “Why do mathematicians write QED in a proof?”
In summary, QED stands for “that which was to be shown or demonstrated” and is used as a way to signal that a proof or argument has been completed. It is often used at the end of a proof as a way to emphasize that the point has been proven and there is nothing left to add. To use QED, one would lay out their premises, conclusion, and then conclude with QED to signal the end of the argument.
Also, people ask
Thereof, What does QED mean in math proof? quod erat demonstrandum
"Q.E.D." (sometimes written "QED") is an abbreviation for the Latin phrase "quod erat demonstrandum" ("that which was to be demonstrated"), a notation which is often placed at the end of a mathematical proof to indicate its completion.
Keeping this in view, Do you have to write QED at the end of a proof?
The answer is: Proof-Writing Tips. There’s a formal or ritualistic structure to mathematic proofs. Begin with "Proof:" and mark the end of your proof with "QED", a box, or some other symbol. QED is from Latin phrase quod erat demonstrandum, meaning "which was to be demonstrated".
Considering this, Why do people write QED? "Q.E.D. is an initialism of the Latin phrase "quod erat demonstrandum" meaning "what was to be shown" or "thus it has been demonstrated." Traditionally, the abbreviation is placed at the end of a mathematical proof or philosophical argument to indicate that the proof or argument is complete."
Considering this, What does QED mean at the end of a proof?
Response: Which was to be demonstrated
Latin abbreviation for quod erat demonstrandum: "Which was to be demonstrated." Q.E.D. may appear at the conclusion of a text to signify that the author’s overall argument has just been proven.
Also asked, What does ‘QED’ mean at the end of a proof?
Answer to this: So the ‘QED’ at the end of a proof, or whatever symbol is used to denote it, is not just there to make your proof look cool; it also serves as a visual ‘end of proof’. "Q.E.D. is an initialism of the Latin phrase "quod erat demonstrandum" meaning "what was to be shown" or "thus it has been demonstrated."
Considering this, Why do we use QED?
Answer to this: But aside from all that, the only other reason to use “Q.E.D.” is to make it easy to see where the proof ends, and if you want to do that, you can just put it right after the rest of the proof; it seems unlikely anybody will have trouble with that. What is the meaning of QED in mathematics?
Also, Is QED a re-statement of a theorem?
As a response to this: Strictly speaking, "q.e.d." (as stated) means something like "aas was to be shown", so (strictly) it is only appropriate if the last thing in your proof, indeed, was the thing to be shown. In Euclid, for example, the last thing is every proof is a re-statement of the theorem.
Similarly, What is a proof & why is it important?
Response to this: It is part of the grammar of mathematical writing/discourse. A proof is a key unit of mathematical discourse. It is important therefore to have efficient markers of the beginning and end of the unit. It doesn’t matter what these are – the specifics are arbitrary. You mention the end of the proof.