How to Prove Math Theorems | 1st Ex: Even + Odd = Odd

Summary

In this video, the presenter introduces the concept of a direct proof by demonstrating a simple yet important theorem: the sum of an even integer and an odd integer is always odd. The proof follows a structured five-step process: stating assumptions, defining key terms (even and odd), manipulating expressions, introducing a new integer to fit the odd form, and concluding that the sum is odd. Through this example, the video illustrates the fundamental approach to constructing direct proofs, which will serve as a foundation for more complex mathematical proofs in future lessons.

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