That's the other definition that I was talking about, and it's equivalent to what I wrote: ', you can only have (a,b) and (b,a) in the relation if a=b.'
Both are correct of course, and that one is the more commonly used, but I finally understand the difference between symmetric, antisymmetric and asymmetric after I wrote the property the way I did in my previous message.
Of course that, if you are able to understand one, you should understand the other one.
Bottom line, everyone understand math in a different way, it's cool to have more than one way to refer to the same property :D