haha, infinite sets, there's a perfect example of a paradox. but regarding counting/sequence, when that distinction became clear to me i started to notice it all through language, i mean, where the semantics of words relates to sequence, or number (or size) there has to be some sense to it. like, really, it should not be chapter 1, you call it the first chapter. first can be represented by 1 but it wouldn't be first if there wasn't a state before it. so that's why they invented zero. because of that implicit contradiciton between count and sequence. it wouldn't make sense to say that the ordinals are like halves, they are integral in the same way, but first has to be nothing, before you can start counting anything. nothing is infinite, also, until it starts, then you have finity... now that's one i've not thought through very much. positive infinity of counting. just because it starts at zero, doesn't mean it has to end. i'd argue that implies it can't.