2008 March 8th, 10:38 AM
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#1 (permalink) |
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only Loeb spaces!
 Moderator 
Join Date: Dec 2004
Posts: 2,078
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How to write a lazy proof (in mathematics)
You too can write a lazy proof! Just use at least one of the following phrases in a key point of your proof.
For an ultra-lazy proof use one of the phrases with an asterisk. 1) It is easy to see that... 2) Obviously... 3) Immediate. * 4) ...and the result follows. 5) As a result, we find that... 6) One easily verifies that... 7) The proof is left to the reader. * 8) The proof is left as an exercise.* 9) ....and the X theorem completes the proof. 10) Clearly... 11) It can be shown that... 12) Trivially... 13) The proof is standard. 14) ...the rest of the proof follows the same line. 15) ...by a trivial argument... Any additions are welcome! (but you have to have actually seen the phrase used in a book or a lecturer's notes)
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"It's easy to have faith in yourself and have discipline when you're a winner, when you're number one. What you've got to have is faith and discipline when you're not yet a winner." Vince Lombardi How to write a lazy proof Teaching yourself how to prove Last edited by reactor : 2008 November 3rd at 12:25 AM. |
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2008 March 8th, 03:13 PM
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#3 (permalink) | |
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TestMagic Guru
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Join Date: Jul 2007
Location: Cambridge, UK
Posts: 1,316
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Quote:
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The Pens have been lifted and the Pages have dried. - recorded by At Tirmidhee. |
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2008 March 8th, 03:18 PM
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#4 (permalink) | |
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only Loeb spaces!
Moderator
Join Date: Dec 2004
Posts: 2,078
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Quote:
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"It's easy to have faith in yourself and have discipline when you're a winner, when you're number one. What you've got to have is faith and discipline when you're not yet a winner." Vince Lombardi How to write a lazy proof Teaching yourself how to prove |
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2008 March 8th, 03:20 PM
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#5 (permalink) | |
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only Loeb spaces!
Moderator
Join Date: Dec 2004
Posts: 2,078
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Quote:
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"It's easy to have faith in yourself and have discipline when you're a winner, when you're number one. What you've got to have is faith and discipline when you're not yet a winner." Vince Lombardi How to write a lazy proof Teaching yourself how to prove |
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2008 March 10th, 05:40 PM
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#6 (permalink) |
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TestMagic Outlier
Join Date: May 2007
Location: US
Posts: 1,169
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We can also "assume without loss of generality" or "to exclude trivial cases assume"... That's only a little lazy, though, I guess.
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Accepted: UConn ($$) WTF?: UWash, GMU No News=Bad News: Cornell, UIUC Rejected: Caltech, Rochester, JHU, WUSTL, Iowa State, SUNY Stony Brook, UMich, Brown |
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2008 March 17th, 06:15 PM
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#7 (permalink) |
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TestMagic Outlier
Join Date: May 2007
Location: US
Posts: 1,169
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I thought of another half-lazy one: "For specificity assume..." (e.g., if proving something about a monotonic function, assume that it is increasing)
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Accepted: UConn ($$) WTF?: UWash, GMU No News=Bad News: Cornell, UIUC Rejected: Caltech, Rochester, JHU, WUSTL, Iowa State, SUNY Stony Brook, UMich, Brown |
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2008 March 19th, 06:51 AM
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#8 (permalink) |
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Eager!
Join Date: May 2006
Location: Boston, MA
Posts: 57
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4 & 5 are my favorites, along with "WLOG, take ... . All other cases are trivial/analogous."
You also have to love the technique, especially common in Rudin, of citing 10+ numbered theorems in a sentence or two, writing one or two expressions, and stating that the desired consequence follows easily. |
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