For a thing to satisfy A=A, it must have a determinate identity – a specific, resolvable magnitude. An infinite set has no terminal boundary and no definite cardinality. It is structurally isomorphic to a proper part of itself. The “whole” infinite set is indistinguishable from a fragment of itself that is missing infinitely many elements.
If the whole were infinite, then there would exist a proper part V ⊂ U such that V is structurally identical to U. By the identity of indiscernible, if U and V share all structural properties, U = V. But by definition, V is a proper part V ≠ U. This yields the formal contradiction U = V ∧ U ≠ V. The identity of the whole collapses.
Therefore, the whole must be finite. It must possess a specific, bounded informational magnitude.
To reject Step 3 is to assert that an infinite set can be identical to a proper part of itself without being identical – a direct A ∧ ¬A contradiction. The processor crashes.