Proof question.

Yeah, true, but the way I read it was that you're starting from x > 1 and supposed to show x^2 > x from that.

I think that's how it should be interpreted, but i must admit I did a double-take when I read it (and the following posts) for the first time!

Yeah, true, but the way I read it was that you're starting from x > 1 and supposed to show x^2 > x from that.

I was starting to give in before you came along!

Well I'm sorry! If a question states "Show that if P then Q" if you start with Q and show P you've not answered the question. The way I've read the OP is that you're given x>1 (P) and supposed to show x^2 > x (Q). But this is a very good example of why you need to be unambiguous in mathematics.

What you don't understand, Noble, is that it does not matter from what point you start to prove this equation, as long as all steps there on will be mathematically correct. If a question starts with "Show that if P then Q", you still would have answered the question starting from Q. It would even be considered a correct and formal proof if you would show that if not Q then not P. According to you this would also be a "wrong start" to the question and be "bad practice". But infact, this is referred to as Reductio ad absurdum. You can read about this here http://en.wikipedia.org/wiki/Reductio_ad_absurdum.

You're square root proof, I haven't looked at yet, but what it seems to be is that if untrue, it probably is due to ambiguities of incorrect mathematical operations concerning the square of both sides of the inequality. I will check it if you insist.

Are you just trolling or being an idiot. If you are asked "Show if P then Q" and you start with Q, you have no answered the question - this is proof 101 . You obviously aren't studying maths at University, because no-one out of the first week would be posting such nonsense.

No insults. No reason to. I am not trolling. I have studied maths beyond university level. "Show if P then Q" does to NO EXTENT state that you have to start with P to prove Q. You COULD EVEN start with 1+1=2 to prove that Q under the assumption that P. Do you have any arguments to support your claim about "proof 101"? No.

I even linked you wikipedia article which shows that "Show if P then Q" can even be answered by stating that if NOT Q then NOT P.
How can an individual be so stubborn and full of judgement and irrational conclusions?

Please, if you don't have any reasonable argument to add to this and want to tell me about bad practice or proof 101 instead. Then go for it but I will not answer. This is embarassing and you are just making a fool of yourself.

Also, proof by contradiction only works... when there is a contradiction . There is no contradiction here.

Exactly, I think Proof 101 needs to go into Room 101.

I don't even understand how it does make a difference. This is the way I see it is:

x > 1 is a fact. Using this we can divide by x to get x > 1 which is true so x^2 > x is true. Or the other way round x > 1 can be multiplied by x as x>1>0, so x^2 > x.

Now I think you're confusing things slightly.

If x>1 then x>0 so we can multiply the inequality x>1 by x on both sides while preserving the direction of the inequality to get x^2 > x as required. This is a proof.

However, you can't "prove" that second inequality by assuming it to be true and then dividing it by something. What you can do is do the division as if it were true and then recognize that if you started from this end position you could construct the proof as given in my previous paragraph.

Now I think you're confusing things slightly.

If x>1 then x>0 so we can multiply the inequality x>1 by x on both sides while preserving the direction of the inequality to get x^2 > x as required. This is a proof.

However, you can't "prove" that second inequality by assuming it to be true and then dividing it by something. What you can do is do the division as if it were true and then recognize that if you started from this end position you could construct the proof as given in my previous paragraph.

No insults. No reason to. I am not trolling. I have studied maths beyond university level. "Show if P then Q" does to NO EXTENT state that you have to start with P to prove Q. You COULD EVEN start with 1+1=2 to prove that Q under the assumption that P. Do you have any arguments to support your claim about "proof 101"? No.

I even linked you wikipedia article which shows that "Show if P then Q" can even be answered by stating that if NOT Q then NOT P.
How can an individual be so stubborn and full of judgement and irrational conclusions?

Please, if you don't have any reasonable argument to add to this and want to tell me about bad practice or proof 101 instead. Then go for it but I will not answer. This is embarassing and you are just making a fool of yourself.

Yet apparently a few days ago you were an IB student?

http://www.thestudentroom.co.uk/showthread.php?p=41976782&highlight=

No insults. No reason to. I am not trolling. I have studied maths beyond university level. "Show if P then Q" does to NO EXTENT state that you have to start with P to prove Q. You COULD EVEN start with 1+1=2 to prove that Q under the assumption that P. Do you have any arguments to support your claim about "proof 101"? No.

Yet, in that post you quoted, Noble made no mention of starting with P… He just said that you shouldn't start with Q (and before you bring up proof by contradiction; that's starting with 'not Q' and that's definitely not the same thing as starting with Q).

He makes a fair point in saying that starting with Q is generally bad practice because it usually requires you to end up proving something stronger (namely the reverse implication too). I agree with you that most proofs are correct on this thread but there's a very fine line between proving it the way you've done, and suggesting that double implications are valid here (as Metaltron suggested earlier in the thread - my only qualms with his posts were the potential to confuse and nothing more.


I'm sure he knows that.



Any further offensive comments will be met with warnings. Please keep your posts firmly on the topic at hand.

I am an IB student, but does that mean that I haven't studied maths beyond universtiy level? Full of assumptions this thread.

Yes but an other assumption would be that, if you have studied maths beyond university level, then that means you know what you are talking about.

In the context you posted, it seemed like formal study, such as a Masters, etc.

I too have studied a tiny amount of undergraduate maths, but I'm no expert, and I think there is a distinct difference between an amateurish interest, and formal academic study.

This was my proof:

$x^2 > x$
$\Leftrightarrow x > 1$ as x > 1 > 0.
$x > 1$ is true, so:
$x^2 > x$ if x >1.

This shows that you don't have to start with x > 1, you can start with x^2 > x. Also, I'm not saying that anybody else's way is wrong, I am just disputing with some people who are saying this method is incorrect.

You can't start with x^2 > x without making a further assumption about x.

$x^2 > x \Rightarrow x(x-1) > 0$

At this point you would like to divide by x to conclude that x-1>0 and hence x>1, but you can't perform that action without assuming that x>0. However, when you stated that x>0 you inferred this from the statement that x>1, which is the thing you're trying to prove!

No you're not trying to prove it, you're given that x > 1.