I can't come to a comfortable conclusion which doesn't make positive, negative, real, imaginary, complex, irrational or transcendental numbers seem much different fundamentally. Zeno (to the best of my interpretation) illustrates a large part of my problem with: "If there are many, they must be as many as they are and neither more nor less than that. But if they are as many as they are, they would be limited. If there are many, things that are are unlimited. For there are always others between the things that are, and again others between those, and so the things that are are unlimited. (Simplicius(a) On Aristotle's Physics, 140.29)" My question started after I read 'Logicomix', which involved Russell's paradox asking about sets containing themselves. After long, confusing and generally baffled discussions with the coaches in the MLC (math learing center) I spent a couple hours a week arguing theories with a specific coach who was interested in philosophy and numbers. Eventually the topic died at how a set can never really contain itself on account of constant change in all things... and how mathematics can and often is structured practically -- where the infinitesimal change in something representing "one thing" isn't ever really a permanent (1), and how all that isn't really worth considering if you just want to figure out how many 1.5ml wine bottles you have. To me it seems like the sets, " A set is a gathering together into a whole of definite, distinct objects of our perception [Anschauung] and of our thought - which are called elements of the set." - Georg Cantor... are all constantly changing in every sense, containing and being contained, and we try to capture them to be used by treating them numerically like unchanging snapshots which stand perfectly still until we can mimic the motion and behavior of the reality. I'm certainly no math major... but it feels like there has to be more on this sort of thing.