quote:

**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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