What about quite easily done?
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)
Last edited by reactor; 11-03-2008 at 12:25 AM.
"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
"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
nope. quod erat demonstrandum stands for "which was to be shown" and concludes a proof without making it less clear.
"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
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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