How to write a lazy proof (in mathematics)

[reactor]

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)

[TruDog]

What about quite easily done?

[asianeconomist]

What about quite easily done?

 

Is that the jocular version of "quod erat demonstrandum".

[reactor]

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).

[reactor]

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.

[buckykatt]

We can also "assume without loss of generality" or "to exclude trivial cases assume"... That's only a little lazy, though, I guess. ;)

[buckykatt]

I thought of another half-lazy one: "For specificity assume..." (e.g., if proving something about a monotonic function, assume that it is increasing)

[wolf87]

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.

[Oikos-nomos]

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...:hmm:

[EconCandidate]

10) Clearly ....(whatever they wanted to prove)

11) It can be shown that ....(yes, but not by me)

[representative_agent]

My favorite is: "Trivially, ...."

[Diplomer]

Proof by break: "The proof will be shown after the break".

...

"As we already proofed before the break, it follows that ..."

 

 

That is my favorite...

[DasGut]

My favorite (from uncyclopedia):

 

Proof by Religion

 

This method of attacking a problem involves the principle of mathematical freedom of expression by asserting that the proof is part of your religion, and then accusing all dissenters of religiously persecuting you, due to their stupidity of not accepting your obviously correct and logical proof.

[Oikos-nomos]

Hahaha!!!

 

My favourite one is Proof by Chuck Norris:

 

Proof by Chuck Norris

If Chuck Norris says the statement is true, then it is true. Anyone who questions it gets roundhouse kicked.

 

And some economists like the Proof by Complexity:

 

Proof by Complexity

Remember, something is not true when its proof has been validified, it is true as long as it has not been disprooved. For this reason, the best strategy is to limit as much as possible the number of people with the needed competence to understand your proof. Be sure to include very complex elements in your proof. Infinite numbers of dimentions, hypercomplex numbers, indeterminate forms, graphs, references to very old books/movies/bands that almost nobody know, quantum physics, modal logic, and chess opening theory are to be included in the thesis. Make sentences in Latin, Ancient Greek, Sanskrit, Ithkuil, and invent languages. Refer to the Cumbersome Notation to make it more complex. Again, the goal: nobody must understand, and this way, nobody can disprove you.

 

Link:

Proof - Uncyclopedia, the content-free encyclopedia