(February 28, 2018 at 4:45 pm)SteveII Wrote:(February 27, 2018 at 11:58 pm)polymath257 Wrote: I bring in set theory because you have postulated an infinite collection of rooms. That collection of rooms *is a set*. That's all that sets are: collections of objects. In particular, the collection of rooms in the HH is an infinite set. Because of this, already adopted the axiom of infinity when you start asking these questions. So, it was not I that begged the question, but you.
And right there is the problem with ALL of your reasoning to date on this subject. An infinite number of rooms is not as 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.
Quote:In mathematics, a set is a collection of distinct objects, considered as an object in its own right. For example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2,4,6}. [opening sentence in the article: https://en.wikipedia.org/wiki/Set_(mathematics)] emphasis added
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?