[throway88989898]

https://en.wikipedia.org/wiki/Halting_problem

https://en.wikipedia.org/wiki/Proof_of_impossibility

https://en.wikipedia.org/wiki/Set_theory#Objections_to_set_t...

[ukj]

Precisely. The point is that ALL operators do actual, physical work.

Work == Energy. Energy == Proof-of-work.

If X is an infinite-byte object then comparing it to itself should take infinite time, whereas determining its identity is O(1)

[ukj]

Also, I didn't start with set theory to get here. I started with Type theory as foundational.

[throway88989898]

It's outside my knowledge space. What are the implications to computability or mathematics?

[ukj]

The law of identity is a blunder. It's the Principle of explosion in disguise.

If one x = x can be trivial to determine But another x = x is infinitely complex then in one single law you have a triviality and infinity.

That's the principle of explosion !