I agree there is a bunch of complexity in generalising Kolmogorov complexity to general infinite strings. However I'm not really trying to do that here, all I w

I agree there is a bunch of complexity in generalising Kolmogorov complexity to general infinite strings. However I'm not really trying to do that here, all I want is enough to back-up the statement I made before, that the complexity of pi is finite. Doing that is much more trivial than what you're talking about. Theres a bunch of fine detail in getting it down to defining an actual number measuring complexity which I don't care about at all, all I care about (in the context of this discussion) is that the number is finite.