[as]

I don't see a coherent argument here, which further suggests that it doesn't mean anything.

Our having a concept of infinity has no metaphysical significance. All our definitions are phrased negatively, by what it's not:

Infinite: That which has no limit. From the Latin 'infinitas', meaning 'unboundedness'.

Try and see if you can define infinity by what it is rather than what it isn't.

[the]

"Infinity is that which can be put in one-to-one correspondence with a subset of itself."

If you're saying that infinity is not directly realizable in what we perceive, then I agree. But this has little to do with how it's defined (or even its metaphysical significance); positive and negative definitions are for all intents and purposes equivalent.

[robg]

What, exactly, do you think I'm trying to argue? To me the question is exactly whether having a concept of infinity has metaphysical significance. I think no good answer is humanly possible. Your definition is just as tautological as anything offered in the positive. That's exactly the problem.

[as]

That's the problem, it's hard to tell what you're saying.

[robg]

Then I've failed... :)

Seriously, I'm not trying to proselytize nor argue. I just find atheism to be an untenable position. It's an attempt to say something while really saying nothing. Problem is, I know the same can be said of theism. But I think the latter is that much more compelling because it starts and ends with one question - "God" - that we can pose to ourselves. Where the answer leads is up to us to decide.