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A basic is an introduction. A fundamental is a foundation. A fundamental is a premise, idea, or fact that an entire system arises from and is based on. A fundamental determines the shape of what arises from it, much as a foundation of a house dictates its layout. A basic is how you introduce people you are teaching to the system. It is a beginning concept, often simplified to assist learning. If a fundamental is the foundation, a basic is the front door to enter the system.
