You have a point. I tend to dislike arguments about mathematics that start with "well, this definition is just a choice"

Me too! Especially as I've just been reading that sequence here about "proving by definition" and "I can define it any way I like"... that's why I tried to make it very clear I wasn't saying that... I also needed to head of the heading off ;)

Anyway - I believe we are just in violent agreement here, so no problems ;)