Gel'fond's Axiom

Gel'fond's Axiom is an assumption related to how certain mathematical functions grow and interact. It proposes that for specific types of functions—particularly those involving exponential and algebraic elements—certain linear combinations will not be zero unless all coefficients involved are zero. In essence, it suggests a form of independence among these functions, implying they don't satisfy unexpected algebraic relations. This axiom plays a role in transcendence theory, helping mathematicians understand which numbers, like certain logarithms or exponentials, are not algebraic and therefore transcendental.