7
$\begingroup$

Is there a Latin phrase that would be used when accepting some statement without providing the proof of such a statement?

For example, say you are working on an elementary number theory proof, and you make the statement "since $p$ is odd, $p^2$ is odd, which we accept [Latin phrase for 'without showing proof']." Obviously this is a simple thing to prove, but in some cases it might be nice to acknowledge that a proof exists and we do not wish to show it.

Could ex facie be used in such a situation ("we accept ex facie that $q$ odd implies $q^2$ odd")? Or failing the existence of a Latin phrase, is there a way that sounds a little less crude than "without proof"?

$\endgroup$
  • 9
    $\begingroup$ Well, there is an English phrase. Why the need for Latin? $\endgroup$ – Qiaochu Yuan Aug 8 '12 at 20:34
  • 8
    $\begingroup$ Why do you want it to be Latin? It will be much more readable simply to write something like "Let's assume as given that such-and-such" or "It can be proved that such-and-such". $\endgroup$ – Henning Makholm Aug 8 '12 at 20:35
  • 4
    $\begingroup$ The request for a Latin phrase is because I feel as if I've encountered one once upon a time, and I don't recall where -- just that I had to ask someone what exactly it was. Also, the English phrasing, "we state without proof that $q$ odd implies $q^2$ odd" seems a little patronizing, as similar wording is used in elementary textbooks for when a concept is deemed to complicated for the reader. I'm looking for a phrase that could be used in place of the dreaded "clearly," except that we acknowledge that proof of the statement exists, rather than hoping it does. $\endgroup$ – Emily Aug 8 '12 at 20:54
  • 15
    $\begingroup$ "The proof is left as an exercise for the reader". $\endgroup$ – Robert Israel Aug 8 '12 at 21:16
  • 8
    $\begingroup$ Just do what the author of my linear programming textbook does and claim that everything is "easy to see". As a bonus, it's a good way to make readers feel bad about themselves. $\endgroup$ – crf Aug 8 '12 at 23:10
5
$\begingroup$

It appears as though ex facie bears the intended meaning. Prima facie has a similar meaning.

$\endgroup$
0
$\begingroup$

Arguendo is close, and might better fit proofs by contradiction, or derivations from a conjecture.

$\endgroup$
-1
$\begingroup$

Are you thinking of a priori?

$\endgroup$
  • $\begingroup$ This is not an answer - you should post it as a comment. $\endgroup$ – Dennis Gulko Oct 15 '13 at 14:56
  • 1
    $\begingroup$ No. A priori means before the fact, which is different. The desired term instead would communicate that we're accepting a result on face value, without detailed examination that the result is true, perhaps because exploration would be a distraction from the intended result, or alternatively that demonstrating the result would be too lengthy. $${}{}$$As an example, consider writing a clever homework solution in an analysis class that uses, say, the Sylow theorems. You wouldn't want to prove them, but you might want to use them. $\endgroup$ – Emily Oct 16 '13 at 16:42
  • 2
    $\begingroup$ @DennisGulko look at the poster's reputation, it takes 50 reputation to post comments. $\endgroup$ – Olivier Bégassat Dec 10 '13 at 2:45
-1
$\begingroup$

Axiom (something that is accepted without proof) ex.: this statement is an Axiom.
Axiomatic, ex.: this statement is axiomatic in every sense.
Axiomatically, ex.: this statement is axiomatically accepted by some.
Note: Of Greek origin but surely used in Latin as well.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.