The axiom of choice is intuitive because its seems one should always be able to take many aggregates of elements and make a new aggregate. The axiom of choice

The axiom of choice is intuitive because its seems one should always be able to take many aggregates of elements and make a new aggregate. The axiom of choice is counter-intuitive because it provides no reason to, in the case of a uniform aggregate, choose one element over another. Nor a reason to suppose in the case of a "complex aggregate" that "choice" is even well-defined. Perhaps one way of thinking of the issue here is the tension between the discrete and continuous. Of course, one can always recombine even inifnite number of discrete things. But what does it mean to "choose" a "point" on a "line" ? Can one "choose" pi? One could, for example, take the view that the very notion of membership, "choice", etc. is conceptually inadequate for handling geometrical matters such as the reals.