03-08-2008, 09:38 AM
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#1 (permalink) |
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only Loeb spaces!
 Moderator 
Join Date: Dec 2004
Posts: 2,072
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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. 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 Since 2004 Reactor features (also) at: Econometric Analysis, 5th Edition ERRATA Last edited by reactor : 05-13-2008 at 09:54 PM. |
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03-08-2008, 02:13 PM
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#3 (permalink) | |
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Loving the game
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Join Date: Jul 2007
Location: Where the grass is greener
Posts: 890
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Quote:
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The Pens have been lifted and the Pages have dried. - At Tirmidhee. |
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03-08-2008, 02:18 PM
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#4 (permalink) | |
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only Loeb spaces!
Moderator
Join Date: Dec 2004
Posts: 2,072
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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 Since 2004 Reactor features (also) at: Econometric Analysis, 5th Edition ERRATA |
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03-08-2008, 02:20 PM
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#5 (permalink) | |
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only Loeb spaces!
Moderator
Join Date: Dec 2004
Posts: 2,072
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Quote:
_ _ _ _ SIG _ _ _ _
"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 Since 2004 Reactor features (also) at: Econometric Analysis, 5th Edition ERRATA |
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03-10-2008, 04:40 PM
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#6 (permalink) |
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TestMagic Guru-in-Training
Join Date: May 2007
Location: US
Posts: 895
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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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"It's like a nerd watering hole in the savanna!" - econphilomath |
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03-17-2008, 05:15 PM
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#7 (permalink) |
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TestMagic Guru-in-Training
Join Date: May 2007
Location: US
Posts: 895
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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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"It's like a nerd watering hole in the savanna!" - econphilomath |
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03-19-2008, 05:51 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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