In the quaint study of Professor Hercule Poirot, a serene silence filled the air, save for the ticking of the mantelpiece clock. The renowned detective, his mustache impeccably groomed and his gray cells poised for action, sat at his desk, surrounded by an assortment of leather-bound tomes and scrolls. His eyes flickered with a hint of anticipation as he embarked upon a seemingly innocent pursuit—a proof that 1+1 equals 2, akin to the mystery he had yet to unravel. Poirot's gaze fell upon the foundational Peano axioms, a set of principles upon which the entire realm of arithmetic was built. Ah, such elegant simplicity, he thought, as he began his voyage into the world of logical deductions. Firstly, he invoked the axiom of identity, which declared that for any natural number 'n,' n equals n. In this case, let us consider '1.' Therefore, 1 = 1. To proceed further, Poirot required the concept of the successor function—a transformative operation that takes a natural nu...