RE: Actual Infinity in Reality?
February 28, 2018 at 5:00 pm
(This post was last modified: February 28, 2018 at 5:04 pm by SteveII.)
(February 28, 2018 at 4:48 pm)polymath257 Wrote:(February 28, 2018 at 4:45 pm)SteveII Wrote: And right there is the problem with ALL of your reasoning to date on this subject. An infinite number of rooms is not a set. The rooms are rooms. Distinct objects in their own right. There is no justification to collect the rooms into some mathematical abstract object and treat them as a block with a different set of rules. Sets only exist on paper--in mathematics.
So we cannot look at the collection of all the rooms? Why not? Whether or not it is 'mathematical', does it make sense to talk about the collection of rooms?
Why would we have to add all the rooms to a set? When we are counting and dividing up bricks to build four sides of a house, do we have to put them in a set to discuss them? What principle are you applying that requires it? Also, set theory is a specialized mathematical concept governed by a whole set of axioms. Why would you have to apply a mathematical concept to a simple accounting of rooms in a hotel? We wouldn't for a 100, 1000 or even 10^10 rooms.