proof!

[sysD]

prove that :

 

 

 

$x=x$

[DrRocket]

  On 2/13/2012 at 4:12 AM, sysD said:

prove that :

 

 

 

$x=x$

 

 

There is nothing to prove. "=" means "is".

[sysD]

incorrect. any takers?

 

EDIT: its not what you think

Edited February 13, 2012 by sysD

[insane_alien]

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.

[D H]

  On 2/13/2012 at 5:51 AM, sysD said:

incorrect. any takers?

Incorrect. Dr Rocket is correct. The identity relationship is reflexive by definition.

 

  Quote

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"?

[ajb]

  On 2/13/2012 at 11:23 AM, insane_alien said:

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".

[sysD]

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

[Cap'n Refsmmat]

$x\neq x$?

[sysD]

that's the one, thanks cap'n.

[D H]

Oh please. We don't need another stupid division by zero "proof" to show that 1=2 or x≠x.

[DrRocket]

  On 2/14/2012 at 1:33 AM, Cap said:

$x\neq x$?

 

 

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.

[sysD]

  On 2/14/2012 at 1:41 AM, D H said:

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.

 

 

 

 

  On 2/14/2012 at 2:15 AM, DrRocket said:

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.

[ajb]

  On 2/14/2012 at 1:28 AM, sysD said:

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.

[the tree]

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?

[Fuzzwood]

The 3rd line already states that 0 = 0

[the tree]

That was the intention yes.

[D H]

  On 2/14/2012 at 4:44 AM, sysD said:

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.

[DrRocket]

  On 2/14/2012 at 1:28 AM, sysD said:

.

 

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".

[the tree]

  On 2/14/2012 at 9:15 PM, DrRocket said:

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.

[tomgwyther]

Long shot:

Has it anything to do with the saying "Sure as eggs is eggs"?

[DrRocket]

  On 2/14/2012 at 9:18 PM, the tree said:

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

[questionposter]

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

[ajb]

  On 2/15/2012 at 3:30 AM, questionposter said:

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".