sysD Posted February 13, 2012 Share Posted February 13, 2012 prove that : [math]x=x[/math] Link to comment Share on other sites More sharing options...
DrRocket Posted February 13, 2012 Share Posted February 13, 2012 prove that : [math]x=x[/math] There is nothing to prove. "=" means "is". Link to comment Share on other sites More sharing options...
sysD Posted February 13, 2012 Author Share Posted February 13, 2012 (edited) incorrect. any takers? EDIT: its not what you think Edited February 13, 2012 by sysD Link to comment Share on other sites More sharing options...
insane_alien Posted February 13, 2012 Share Posted February 13, 2012 If x!=x then x=x is wrong 1=1 and not 1!=1 then x!=x is also wrong. x!=x leads to contradictions therefore x=x is true. Link to comment Share on other sites More sharing options...
D H Posted February 13, 2012 Share Posted February 13, 2012 incorrect. any takers? Incorrect. Dr Rocket is correct. The identity relationship is reflexive by definition. EDIT: its not what you think Oh really. Perhaps you should tell us what you think then. What set, what axioms, and what definition of equality are you using that makes you think that "it's not what you think"? Link to comment Share on other sites More sharing options...
ajb Posted February 13, 2012 Share Posted February 13, 2012 1=1 and not 1!=1 then x!=x is also wrong. We have not been informed what kind of objects x are. They may not be numbers. DrRocket is right there is nothing to prove. The statement x=x is the reflexive relation of "equals". We understand this as being an intrinsic property of "equals". Link to comment Share on other sites More sharing options...
sysD Posted February 14, 2012 Author Share Posted February 14, 2012 (edited) I'm serious guys. Its very counter-intuitive. I can't give out any hints though; I know someone here is smart enough to prove it. OH Crap. Sorry, I posted the wrong equation. I can't edit the OP so here it is: ________________________________________________________________________ Prove that: x=/=x x is in the set of Real Numbers [couldnt figure out the math script notation for "does not equal..." if a mod would like to help me out i'd appreciate it.] Edited February 14, 2012 by sysD Link to comment Share on other sites More sharing options...
Cap'n Refsmmat Posted February 14, 2012 Share Posted February 14, 2012 [math]x\neq x[/math]? Link to comment Share on other sites More sharing options...
sysD Posted February 14, 2012 Author Share Posted February 14, 2012 that's the one, thanks cap'n. Link to comment Share on other sites More sharing options...
D H Posted February 14, 2012 Share Posted February 14, 2012 Oh please. We don't need another stupid division by zero "proof" to show that 1=2 or x≠x. 1 Link to comment Share on other sites More sharing options...
DrRocket Posted February 14, 2012 Share Posted February 14, 2012 [math]x\neq x[/math]? A valid proof of a patently false assertion can only be made using an inconsistent set of axioms, in which case any assertion is both true and false. Inconsistent axiom systems are not very interesting. The only alternative was alluded to by DH, namely do something stupid and call it clever. Link to comment Share on other sites More sharing options...
sysD Posted February 14, 2012 Author Share Posted February 14, 2012 Oh please. We don't need another stupid division by zero "proof" to show that 1=2 or x≠x. You're close, but that's not it. I promise you its something very simple and every day - yet I don't think many would think to apply it here. A valid proof of a patently false assertion can only be made using an inconsistent set of axioms, in which case any assertion is both true and false. Inconsistent axiom systems are not very interesting. The only alternative was alluded to by DH, namely do something stupid and call it clever. Try it out, as a thought experiment. You may be surprised. Link to comment Share on other sites More sharing options...
ajb Posted February 14, 2012 Share Posted February 14, 2012 I can't give out any hints though; I know someone here is smart enough to prove it. Post your "proof" and we can then examine it. Link to comment Share on other sites More sharing options...
the tree Posted February 14, 2012 Share Posted February 14, 2012 I'm willing to bet it's along the lines of x = x x^2 = x*x x^2 - x^2 = x*x - x^2 (x + x)(x - x) = x(x - x) x + x = x 2x = x x != x which I think we can all agree is utter rubbish. Do we really need to pursue that any further? Link to comment Share on other sites More sharing options...
Fuzzwood Posted February 14, 2012 Share Posted February 14, 2012 The 3rd line already states that 0 = 0 Link to comment Share on other sites More sharing options...
the tree Posted February 14, 2012 Share Posted February 14, 2012 That was the intention yes. Link to comment Share on other sites More sharing options...
D H Posted February 14, 2012 Share Posted February 14, 2012 You're close, but that's not it. I promise you its something very simple and every day - yet I don't think many would think to apply it here. You cannot prove x≠x. It is nonsense. Mathematics is extremely intolerant of nonsense. It is of course possible to arrive at a result by means of some calculation. However, this does not mean you have proven that x≠x. It instead means that - You made a mistake somewhere along the way in getting to that result, or - One or more of your assumptions is invalid. This latter possibility leads to a very powerful mathematical tool for proving or disproving hypotheses, powerful precisely because mathematics is extremely intolerant of nonsense. It's called proof by contradiction. Link to comment Share on other sites More sharing options...
DrRocket Posted February 14, 2012 Share Posted February 14, 2012 . I can't give out any hints though; I know someone here is smart enough to prove it. Nope. There is only one person here dumb enough to call any such nonsense a "proof". Link to comment Share on other sites More sharing options...
the tree Posted February 14, 2012 Share Posted February 14, 2012 There is only one person here dumb enough to call any such nonsense a "proof".I reckon if you really trawled through the forums then you'd find a handful. Link to comment Share on other sites More sharing options...
tomgwyther Posted February 15, 2012 Share Posted February 15, 2012 Long shot: Has it anything to do with the saying "Sure as eggs is eggs"? Link to comment Share on other sites More sharing options...
DrRocket Posted February 15, 2012 Share Posted February 15, 2012 (edited) I reckon if you really trawled through the forums then you'd find a handful. Agreed. I was referring to this particular thread. (Added in edit: And at the time I wrote it. I am not responsible for the effect on the truth of my assertion that may be caused by any latecomers.) If you were to trawl Philosophy your net might not take the load. Edited February 15, 2012 by DrRocket Link to comment Share on other sites More sharing options...
questionposter Posted February 15, 2012 Share Posted February 15, 2012 (edited) When you end an actual mathematical proof, don't you end it with "thus" followed by an equation such as "x=x"? I don't think you can go any further. I think any other proof would be needlessly adding things. x=x because there isn't anything saying it isn't, x is by the identity of x equal to x. Edited February 15, 2012 by questionposter Link to comment Share on other sites More sharing options...
ajb Posted February 15, 2012 Share Posted February 15, 2012 x=x because there isn't anything saying it isn't, x is by the identity of x equal to x. Really it comes down to the basic fundamental and natural properties of equivalence relations. Very loosely, an equivalence relation, lets say on elements of some set, gives us a way of saying if the elements are "alike" or not. We can then break-up the set into smaller collections of equivalent elements. These are the equivalence classes. Don't panic, all I am really saying is we can define in many many ways how two elements can in essence be the "same" and this will of course depend on the context. Anyway, I think we would end up being very confused if we said that "x is not like x with respect to some property that x has". Link to comment Share on other sites More sharing options...
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