[DrRocket]

the tree, on 14 February 2012 - 09:18 PM, 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.

This post has been edited by DrRocket: 15 February 2012 - 04:13 AM

[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.

This post has been edited by questionposter: 15 February 2012 - 03:32 AM

[ajb]

questionposter, on 15 February 2012 - 03:30 AM, 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".