The Infinite Principle: The Mathematics of Optimism

This paper introduces the infinite principle, a mathematical framework demonstrating that optimism is rationally obligatory when comparing bounded and unbounded outcomes. Rooted in expected value theory, the principle proves that any option with unbounded upside-no matter how improbable-mathematically dominates alternatives with bounded outcomes, provided the downside is finite and the probability of success is nonzero. This transforms optimism from a subjective disposition into an objective necessity.