Syntax wrote:
∀x1∈N => 1xN
Should cover everything (naturally)
I'm not sure. I think (?) you meant to write something inductive like:
∀x x∈ℕ ⇒ x+1∈ℕ (?)
...but you (probably) actually meant something simpler like:
∃x x∈ℕ ∧ P(x)
...where P(x) means "
x is the correct number of rooms in TSS"
. (You don't need to use induction to generate ℕ, because ℕ must already have been defined for you to refer to it as the domain of discourse.)
∃x x∈ℕ ∧ P(x) should be true as long as both: P(x) is formalized in first-order predicate calculus, and P(x) is true for some finite x.
however I still hold out hope that there are uncountably many rooms
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