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Proofs and show that.

Whag is the difference? When you have a proof, do u derive the result and prove its truth. And with a show that do u show that it is true. I get mixed up everyday thinking about. Can someone give an explicit definition with examples ie. when given an inequality? or expression?!


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Original post by physicsmaths
Whag is the difference? When you have a proof, do u derive the result and prove its truth. And with a show that do u show that it is true. I get mixed up everyday thinking about. Can someone give an explicit definition with examples ie. when given an inequality? or expression?!


There is no difference.
To me, if a question says "show that ..." that means I take some starting point as a given (for example, one of the Maxwell equations for EM) and apply some processes to it until I get the result asked for. This may just be a single line of calculations over several steps or it may require some natural language explanation of the methods, or references to the symmetry of the problem to simplify it. I was trained a physicist though, so obviously that's a bit different. I never did any proofs but I assume you would start by stating axioms/lemmas/corollaries etc and every step must follow with infallible logic from one to the next until the result is obtained. I suppose from my perspective the different could be simplified by saying 'show that' is an exercise in equation manipulation whereas 'prove that' is an exercise in logic.

We were never asked to prove anything as physics students because nothing in physics has been proven as everything relies on the way we perceive the world around us which is not necessarily true. Even in the maths courses we did the lecturers weren't allowed to ask "prove that" questions because we lacked the skills/vocabulary to do it properly, even for purely mathematical questions with no basis in physics.
(edited 9 years ago)
Original post by Manitude
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Even in the maths courses we did the lecturers weren't allowed to ask "prove that" questions because we lacked the skills/vocabulary to do it properly, even for purely mathematical questions with no basis in physics.

That's a bit strange. They essentially suppressed your knowledge.
Original post by physicsmaths
Whag is the difference? When you have a proof, do u derive the result and prove its truth. And with a show that do u show that it is true. I get mixed up everyday thinking about. Can someone give an explicit definition with examples ie. when given an inequality? or expression?!


Posted from TSR Mobile


Proof is much stronger than show that
You need to begin at one point and move to the desired result

Show that can be done by example

Here are 2 SIMPLE examples

Prove that the sum of 3 consecutive integers is divisible by 3

Let n be an integer

Therefore n, n+1, and n+2 are consecutive integers

n + (n+1) + (n+2)

= 3n + 3

= 3(n+1)

therefore divisible by 3



Show that the point (3,2) lies on the line y = 2x - 4

2*3 - 4

= 2

therefore (3,2) lies on y = 2x - 4

Original post by TenOfThem
..

I think prove and show that are interchangeable in both of those examples..
Original post by Jooooshy
I think prove and show that are interchangeable in both of those examples..


I was taught that there is a difference

Perhaps in modern parlance there isn't
Original post by TenOfThem
Proof is much stronger than show that
You need to begin at one point and move to the desired result

Show that can be done by example

Here are 2 SIMPLE examples

Prove that the sum of 3 consecutive integers is divisible by 3

Let n be an integer

Therefore n, n+1, and n+2 are consecutive integers

n + (n+1) + (n+2)

= 3n + 3

= 3(n+1)

therefore divisible by 3



Show that the point (3,2) lies on the line y = 2x - 4

2*3 - 4

= 2

therefore (3,2) lies on y = 2x - 4

I agree with the people saying you could exchange "show" and "prove" here without being incorrect.

However, I also agree that "prove" would be more usual in the first case, and "prove" would be decidedly unusual in the second case.

I think it's fair to say that the more "general" the result, the more likely you are to see "prove" rather than "show".

[Although one cynical part of me is inclined to say "the difference between 'prove' and 'show that' is that lecturers prove, and examinees 'show that'!"]
Original post by DFranklin
I agree with the people saying you could exchange "show" and "prove" here without being incorrect.

However, I also agree that "prove" would be more usual in the first case, and "prove" would be decidedly unusual in the second case.

I think it's fair to say that the more "general" the result, the more likely you are to see "prove" rather than "show".


[Although one cynical part of me is inclined to say "the difference between 'prove' and 'show that' is that lecturers prove, and examinees 'show that'!"]


Perhaps this is what I meant :smile:

I would certainly not use prove for the second one


However - I was taught that proof requires greater rigour

Take a trig identity
If I were asked to prove I would need to start with one side and demonstrate that it could become the other side
If I were asked to show I would happily mess with both sides until I had the same thing
Original post by Khallil
Even in the maths courses we did the lecturers weren't allowed to ask "prove that" questions because we lacked the skills/vocabulary to do it properly, even for purely mathematical questions with no basis in physics.

That's a bit strange. They essentially suppressed your knowledge.


The justification was that we were doing physics degrees, not mathematics degrees so it would have been unnecessary knowledge for the degree as physics doesn't use proofs. Instead we mainly learnt how to do the calculations and manipulations necessary to do the physics. The people who did "physics with maths" did proofs, obviously, but only in their maths modules.
Original post by TenOfThem
Proof is much stronger than show that
You need to begin at one point and move to the desired result

Show that can be done by example

Here are 2 SIMPLE examples

Prove that the sum of 3 consecutive integers is divisible by 3

Let n be an integer

Therefore n, n+1, and n+2 are consecutive integers

n + (n+1) + (n+2)

= 3n + 3

= 3(n+1)

therefore divisible by 3



Show that the point (3,2) lies on the line y = 2x - 4

2*3 - 4

= 2

therefore (3,2) lies on y = 2x - 4


yeh this is the way i was taught to do them. The reason i had to ask was that say you have a question such as prove that if a,b>0 that the sqr root of ab is less then or equal to < (a+b)/2
i could square both sides and simplify to a^2 -2ab+B^2>0 which is always true as this quadratc is a perfect square hence always greater then 0.
Or i could start with (roota - rootb)^2 >0 which would derive to rootab<(a+b)/2
ehich method are they looking for.
the first method has shown its true? and the second method has proven it!?




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Original post by Manitude
To me, if a question says "show that ..." that means I take some starting point as a given (for example, one of the Maxwell equations for EM) and apply some processes to it until I get the result asked for. This may just be a single line of calculations over several steps or it may require some natural language explanation of the methods, or references to the symmetry of the ******* to simplify it. I was trained a physicist though, so obviously that's a bit different. I never did any proofs but I assume you would start by stating axioms/lemmas/corollaries etc and every step must follow with infallible logic from one to the next until the result is obtained. I suppose from my perspective the different could be simplified by saying 'show that' is an exercise in equation manipulation whereas 'prove that' is an exercise in logic.



That's a good way of thinking about it.
Reply 12
Original post by TenOfThem
Perhaps this is what I meant :smile:

I would certainly not use prove for the second one


However - I was taught that proof requires greater rigour

Take a trig identity
If I were asked to prove I would need to start with one side and demonstrate that it could become the other side
If I were asked to show I would happily mess with both sides until I had the same thing


I'm not too sure what you mean by greater rigour (unless you mean more clear explanation?). Arguably if you do a "Show that" with less mathematical rigour than you'd do a "Prove that" version of the exact same question you haven't rigorously shown what you've been asked to show. Either way it's massively ambiguous and someone would have to put some arbitrary line separating what's a "Show that" and what's a "Prove that" of the same problem (which would be a nightmare) so I think generally they mean the same thing and it's more a choice of which term fits better.

For example, if in an exam you wanted to have the examinees both state and prove/show the DCT holds you would write "State and prove the Dominated Convergence Theorem" - clearly interchanging "prove" for "show" here isn't really available because you'd have to state DCT for them and statements such as "State and show the Dominated Convergence Theorem is true" are far more unclear than "State and prove...".
Original post by Noble.
I'm not too sure what you mean by greater rigour (unless you mean more clear explanation?). Arguably if you do a "Show that" with less mathematical rigour than you'd do a "Prove that" version of the exact same question you haven't rigorously shown what you've been asked to show. Either way it's massively ambiguous and someone would have to put some arbitrary line separating what's a "Show that" and what's a "Prove that" of the same problem (which would be a nightmare) so I think generally they mean the same thing and it's more a choice of which term fits better.


My example indicated what I meant by rigour :smile:
Reply 14
Original post by TenOfThem
My example indicated what I meant by rigour :smile:


It would help if I read your whole post wouldn't it? :lol:

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