what is the point of proofs?
Proofs are used to come up with many useful theorems.
but will i even need them after high school?
It depends on your career path.
The point of proofs in various fields of study, especially in mathematics and logic, is to provide rigorous and logical justification for claims or statements. Proofs allow us to establish the truth or validity of a specific statement or theorem, giving us certainty about its correctness. The goal of a proof is to convince others (and ourselves) that a certain statement is always true under certain assumptions or conditions.
Proofs serve several purposes:
1. Verification: Proofs help us verify the truth of a statement or proposition. They offer a systematic way to confirm that a claim holds true in all cases.
2. Explanation: Proofs provide a deeper understanding of why a particular result or theorem is true. They help us uncover hidden connections between concepts, establish logical relationships, and reveal the underlying structure of mathematical or logical systems.
3. Communication: Proofs are essential for sharing knowledge and ideas within the academic community. They allow researchers to present their findings and discoveries in a clear, concise, and rigorous manner, ensuring their work can be understood and evaluated by others.
4. Foundation: Proofs form the building blocks for further developments in a field. They serve as the foundation on which more advanced concepts, results, and theories are constructed.
To construct a proof, one needs to follow a logical sequence of steps, starting from a set of assumptions or axioms and applying a series of logical deductions or mathematical operations. The ultimate goal is to demonstrate a logical flow of reasoning that leads inevitably to the desired conclusion or result.