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When being asked to justify some conclusion, is it same as to prove it?

My memory tells me that "justify" has been used to describe some informal verification, not necessarily formal proof. I wonder if it is true? If yes, in what sense is "justify" informal? For example, only need to prove necessarity not sufficiency?

Thanks and regards!

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It probably depends strongly on context. In my experience it means anything from "provide some evidence" to "prove." –  Qiaochu Yuan May 30 '11 at 14:15
@Qiaochu: Thanks! Do you mean necessary condition of the conclusion by "evidence"? –  Tim May 30 '11 at 14:26
Doesn't that depend on what you're being asked to justify? –  Qiaochu Yuan May 30 '11 at 15:15

3 Answers 3

up vote 4 down vote accepted

A computation, properly laid out, is of course a proof. However, many students, after years of multiple choice tests, have learned to take the point of view that the answer is the only thing that matters.

"Justify" can be a reminder that the problem will be graded carefully, that (contrary to their usual experience) a slapdash computation will not necessarily get full marks.

I do not think that "justify" carries any connotation of "you need only show necessity but not sufficiency."

"Prove," in a course context, can often mean that a more or less specific set of tools should be used. "Justify" has a more informal feel, but I do not think of it as carrying a lower level of precision.

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Yes, in hindsight this agrees with my experience as well. I guess one interpretation of "justify" is "make sure to use words." –  Qiaochu Yuan May 30 '11 at 18:16

To me, "justify" means to lay out the mathematical thought process step by step, so that the line from the starting point to the ending point is connected.

It is a bit less formal than a proof, which has certain logical requirements, but it means, "show enough work so that I know that you get the whole thing."

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"Justify," just like its buddy "show," really means "prove."

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