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Thread: How to write a lazy proof (in mathematics)

  1. #1
    only Loeb spaces! reactor's Avatar
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    How to write a lazy proof (in mathematics)

    Sponsored Ad:
    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

  2. #2
    An Urch Guru Pundit Swami Sage
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    What about quite easily done?
    University of Wisconsin-Madison--Leaving with a master's degree

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    An Urch Guru Pundit Swami Sage asianeconomist's Avatar
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    Quote Originally Posted by TruDog View Post
    What about quite easily done?
    Is that the jocular version of "quod erat demonstrandum".
    The Pens have been lifted and the Pages have dried. - recorded by At Tirmidhee.

  4. #4
    only Loeb spaces! reactor's Avatar
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    Quote Originally Posted by TruDog View Post
    What about quite easily done?
    Sounds good and I think that some of my lecturers use it often but I have not seen it written (yet).
    "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

  5. #5
    only Loeb spaces! reactor's Avatar
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    Quote Originally Posted by asianeconomist View Post
    Is that the jocular version of "quod erat demonstrandum".
    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

  6. #6
    TestMagic Outlier buckykatt's Avatar
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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.
    Attending: UConn

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    TestMagic Outlier buckykatt's Avatar
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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)
    Attending: UConn

  8. #8
    Eager! wolf87's Avatar
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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.

  9. #9
    Preparing for collision Oikos-nomos's Avatar
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    A good one that i hate is "...and with some simple algebraic manipulations we have..." , it usually means that you have to write half proof by yourself...

  10. #10
    At Wisconsin-Madison
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    10) Clearly ....(whatever they wanted to prove)
    11) It can be shown that ....(yes, but not by me)
    Currently at Wisconsin-Madison

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