Difference between approach for show that and prove that

[rollcast]

Difference between approach for show that ... and prove that ...

Whats the difference between how you solve a problem that involves showing or proving something?

For example what would be the difference between the solution to:

"Show that $\sin\theta(2cos\theta+sin\theta)$ can be written as $3tan\theta$ "

and


"Prove that $\sin\theta(2cos\theta+sin\theta) = 3tan\theta$ "

Admittedly that's a pretty poor and basic example.

To me the solution to both of them should be the same or is there any difference?
Thanks
A

 

[DrewD]

"Show" is usually a specific example, where as "prove" is general. It would be silly (as you note) to ask the second version. If there is a general difference in approach, I would say that if I see "show that" I look for specific instances. If I see "prove that" I look for general theorems. But obviously there may be exceptions to that.

 

[disregardthat]

Prove, show, demonstrate; all synonyms.

 

[Stephen Tashi]

Whats the difference between how you solve a problem that involves showing or proving something?

A common situation is that course materials have one set of standards for a proof and if the materials wish to make it clear that they want something more concise and abbreviated than those standards, they say "show" instead of "prove". There is no universal interpretation for "show" vs "prove", just as there is no universal standard for how much detail that a course wants in proofs. Each textbook and instructor may do things differently.

 

[micromass]

Show and prove usually mean the exact same thing.

 

[dodo]

Show and prove usually mean the exact same thing.

After agreeing with the above, I'd like to quote part of the assessment guide of the UK's Open University (your mileage *will* vary for your institution, so asking your teacher was an excellent suggestion):

[...] As a guide, we use the following wording with the interpretations shown:
* write down or state means 'write down without justification';
* find, determine, calculate, explain, derive or evaluate means that we require you to show all your working when writing out your answer;
* prove, show or deduce means 'justify each step': in particular, if you use a definition, result or theorem to go from one line to the next, you must state clearly which fact are you using -- for example, by quoting the relevant unit and page or by giving a handbook reference -- and you should also check that all the relevant conditions hold.

 

[HallsofIvy]

"Show" is usually a specific example, where as "prove" is general. It would be silly (as you note) to ask the second version. If there is a general difference in approach, I would say that if I see "show that" I look for specific instances. If I see "prove that" I look for general theorems. But obviously there may be exceptions to that.

No. To use the given example, if x= 0, it is true that $sin x(cos x+ 2sin x)= 0= 3 tan x$ but that does not in any sense "show" that the given statement is true for all x.

If x= 0, sin x= 0= 1- cos x but that obviosly does NOT "show" that "sin x= 1- cos x".

 

[rollcast]

Thanks for your replies.

For our maths exams a show that question generally involves them giving you some sort of complicated expression and you have to step by step alter it (I say alter it because sometimes the process of getting the second expression is more complicated than the original was) until you end up with the second expression they give you.

Prove that questions tend to be based around geometry questions or sometimes they explain some of "number trick" and you have to work out an algebraic expression for it which shows it works / doesn't work.

Thanks again
A.

 

[epenguin]

'Show' is a cop-out for lazy writers of textbooks and pop science books who don't show you a damned thing but just tell you 'it can be shown'.

Sometimes they tell you it can be proved but the cop-out is more obvious in that case so they are more inhibited for saying that and you see it less often.

 

[mathwonk]

I use "show" sometimes because some students are frightened by the word "prove", but to me they mean the same.