MHB Don't "Obvious" Your Way Out of This Proof

[Dustinsfl]

So a student used the phrase "it is obvious.." in a proof. What is a nice why to say that equates to bs and you don't actually know how to finish proving it?

 

[MarkFL]

Personally I feel it is okay to state "it is obvious" if in fact it is, or can easily be shown. Otherwise, it should be shown, IMHO.

Sometimes a person writing a proof fails to realize that their readers, who may not have been studying the topic as extensively as the author, simply may not be in the same mindset to find whatever it is, to be quite so obvious.

I have heard many complaints on the use of this phrase in texts over the years, and I have even quipped that when I read "it is obvious" I know I will most likely find it anything but! (Rofl)

 

[Dustinsfl]

Personally I feel it is okay to state "it is obvious" if in fact it is, or can easily be shown. Otherwise, it should be shown, IMHO.

Sometimes a person writing a proof fails to realize that their readers, who may not have been studying the topic as extensively as the author, simply may not be in the same mindset to find whatever it is, to be quite so obvious.

I have heard many complaints on the use of this phrase in texts over the years, and I have even quipped that when I read "it is obvious" I know I will most likely find it anything but! (Rofl)

The assignment was to prove it not state it is obvious. They need to show that they know it is obvious and it is anything but obvious.

 

[MarkFL]

I didn't mean it's okay to merely state the entire intended result is obvious, I meant that only for a minor step in the proof.

Can you show what the student was asked to prove and what their proof was?

 

[Dustinsfl]

My office mate posted the question:
http://www.mathhelpboards.com/f14/indicial-notation-levi-cevita-tensor-3239/

 

[I like Serena]

Wikipedia's style guide says that such phrases should be avoided (here):
"Clearly, obviously, naturally, and of course all presume too much about the reader's knowledge and perspective and are often excess verbiage."

 

[Nono713]

Wikipedia's style guide says that such phrases should be avoided (here):
"Clearly, obviously, naturally, and of course all presume too much about the reader's knowledge and perspective and are often excess verbiage."

I use "clearly" sometimes but I always make sure what I'm about to consider clear is sufficiently trivial for the reader to which the post is addressed to understand. When it comes to school work, I don't use it except for extremely basic stuff (why take risks).

I'm not a teacher but if a student gave me a proof with the main theorem stated as obvious, I'd probably ask him to elaborate, maybe he doesn't know how to prove it and is taking his chances, or perhaps he is a genius and has a simple and elegant argument :)

In addition, in mechanical proofs (like those so often encountered in introductory mathematics) that have many individual but similar cases to consider, I've often been guilty of proving the first case, and then briefly adding "the remaining cases can be checked in the same way" and ending the proof there. In my opinion one should not penalise if students do that in this particular context, no value is added to the proof by repeating the same argument N times.

 

[I like Serena]

I believe that if something is clear, it should also be possible to state why it is clear, without really using more words.
If that is not possible, then IMO it is not clear.

By now I've learned that when a word like obviously is used, it usually means (or should mean) that it follows from a definition.
A lot of students do not know all the definitions properly yet however, which is usually their key problem.
They also do not know yet that obviously is used in that way.

If something follows from the definition, I prefer to say that instead of making a student feel intimidated and stupid.
I've been training myself to avoid those words by either just leaving them out, or by saying something that is more to the point.

Oh, and I've also seen students use it - usually when they are totally clueless.
Since they would have seen it used by others in a reasoning they did not understand, they try to use it as an escape.
Sometimes it is even true, although I would prefer to discourage such usage.

 

[Dustinsfl]

In addition, in mechanical proofs (like those so often encountered in introductory mathematics) that have many individual but similar cases to consider, I've often been guilty of proving the first case, and then briefly adding "the remaining cases can be checked in the same way" and ending the proof there. In my opinion one should not penalise if students do that in this particular context, no value is added to the proof by repeating the same argument N times.

They didn't prove any part of it. They just said it is clearly true.

 

[Fantini]

Then obviously their grading should be zero. (Rofl) It is easy to see they had this coming. Clearly, if they had sketched some proof, it would have been different. (Drunk)

 

[Dustinsfl]

Then obviously their grading should be zero. (Rofl) It is easy to see they had this coming. Clearly, if they had sketched some proof, it would have been different. (Drunk)

My original question was a nice way to say this is bs but it got off track with everyone discussing the meaning of the word.

 

[MarkFL]

It was unclear to me that you meant the entire proof consisted of this statement. I thought you were referring to just a step in the proof.

Of course just saying "it is obvious" as the entirety of the proof deserves no credit.

 

[hmmmmm]

Could you not just write "this need explanation" or why "why is this clear" or even just say to them thatyou can't write "this is obviou" you need to explain why it is obvious (i.e. give a proof)

I don't think it's too hard to do that and not be rude, you hardly need to walk up to them as say this us is bs you don't know what your talking about

 

[Dustinsfl]

Could you not just write "this need explanation" or why "why is this clear" or even just say to them thatyou can't write "this is obviou" you need to explain why it is obvious (i.e. give a proof)

I don't think it's too hard to do that and not be rude, you hardly need to walk up to them as say this us is bs you don't know what your talking about

Trust me it was bs. They didn't try or felt that could get by with a cop out answer. This is a graduate class.

 

[Turgul]

There is no particular requirement to be harsh. If it is a graduate course, they should be expecting to get no credit for that (part of the?) problem. If I were to find someone claiming something is obvious anywhere I didn't agree with, I would just underline or circle the claim and write a note saying "This needs explanation."

Whether they simply did not have the time or inclination to do the problem (they're adults, they are entitled not to do something if they are willing to face the consequences) or if they were trying to elicit a response from you, this works best. If the didn't do it because they didn't want to or have time, you've just pointed out what they already know and it is clear why they lost points. If they were actually trying to be a jackass (which is unusual), it's best to act professionally and pay no extra heed to it. The simple presence of red ink will get your displeasure across well enough.