Category talk:Equivalence Relations

I'm not sure the best place to post this, but I'm after a proof that I just can't solve. Basically, that functions commuting is an equivalence relation (specifically, the transitive property that if fg = gf & gh=hg then fh=hf). I intuitively think it is one, I certainly can't think of a counter example, but I can't prove it. Is this a proof that could go in this category? Thanks!--Mathemagician 06:06, 23 October 2011 (CDT)

I am sorry. When we take $f,g,h$ to be matrices (which are linear maps), then taking $g$ to be the identity matrix will generally disprove this. If the functions you consider are from a more specified realm, I would like to know their domains and what the multiplication of functions is. Last of all, welcome to PW. --Lord_Farin 06:09, 23 October 2011 (CDT)

Of course - I am being stupid! Any identity function commutes with everything, so any identity function in any realm will disprove it. Silly me! Thanks for the welcome--Mathemagician 06:11, 23 October 2011 (CDT)