The discussion centers on the philosophical and mathematical implications of infinity, particularly in relation to subsets. It asserts that an infinite volume, such as water, can still be considered infinite even if it contains finite objects like rocks. The conversation references Hilbert's hotel to illustrate that removing an infinite subset (even numbers) from a larger infinite set (natural numbers) still results in an infinite set (odd numbers). The participants emphasize that infinity is a concept that transcends physical limitations, suggesting that even with boundaries or finite elements, infinity remains intact.
PREREQUISITESMathematicians, philosophers, cosmologists, and anyone interested in the foundational concepts of infinity and its implications in both mathematics and the physical universe.
Infinity is a mathematical concept. If you can put rocks in it, you speak about something which exists within the universe, and then - in case it should be infinite - all rocks are already in it.ddjj77 said:Is infinity truly infinite if it has something else in it?
Put differently, say there's an infinite volume of water that has some rocks in it, is the volume of water truly infinite? Though there's a place where there's no water?