Create a free Team What is Teams? Learn more. What is the meaning of the expression Q. Ask Question. Asked 6 years, 8 months ago. Active 6 years, 8 months ago. Viewed 20k times. Jr Antalan.
Jr Antalan Jr Antalan 2, 2 2 gold badges 11 11 silver badges 27 27 bronze badges. Show 12 more comments. Active Oldest Votes. Jim Jim It's a phrase that Euclid put at the end of his theorems. Which pizza Flavour is best in taste? Walker Darrah. Agustin Hulme. What is the highest calorie food at Cheesecake Factory? Jarrod Stonier.
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It makes proofs more readable. Show 14 more comments. Active Oldest Votes. The key thing is that it costs little and adds to efficiency and accuracy of communication. Mark Bennet Mark Bennet Add a comment. Why indicate the end of a proof? Several reasons: In a book where there is both discussion and proof indicating the end of the proof prevents a reader from thinking that the following discussion is still part of the proof.
I thought it was Halmos. I've edited accordingly. Let's contrast two very different ways of explaining how we know something. Well, let's look at a few things that can derail the above style: The proof is long enough a new paragraph ought to start when it's finished; and, just in case the next paragraph might be expected to also be a part of the proof, you need to make clear it isn't.
Proofs can be long because no shorter option exists, because you as author don't know of one, or because the sort of compression I used above asks too much of the reader. I suspect my example above would be a bit much for most people if it was the first time they ever see the FTA proven.
Heck, even needing to make one or more equations display-line can break the eye's definition of a paragraph too much to get away with the "conversational" approach I described. The proof needs to be stretched out to familiarise the reader with techniques it's meant to illustrate. It might give its name to the chapter you're reading, even if most of the chapter discusses its significance while the proof itself is half a page. If I had appended "This is called the fundamental theorem of arithmetic" to example 1, I would have buried the lede.
And the reader might wonder whether both parts or just the second one were the theorem; and if I'd said "these two results", some readers wouldn't have parsed it so as to know what two results I mean. So either way, I can't win. You're welcome to invent your own examples of when the name needs to be up front, but the reasons why would vary. Formatting is of course an art, where any number of concerns can come up from time to time.
Think about the type of proof you are doing and its main steps. What are its assumptions? Make sure to state them first. Definitions are critical in connecting one concept to another. Use them. You do not necessarily have to rewrite the entire definition within your proof, just refer to it.
Having trouble getting started on a proof? Write out its main steps and the definitions of the terms involved. How can you use those definitions? Work on scrap paper first. Keep symbols to a minimum in written work they are great for presentations at the board. Avoid using symbols at the beginning of a sentence.
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