A theorem is a mathematical statement that has been proven to be true based on deductive reasoning from previously established truths, axioms, or other theorems. Option D is correct.
A theorem in mathematics is a statement that has been rigorously proven to be true based on logical reasoning from established principles. It is a fundamental building block of mathematical knowledge, derived from axioms and previously proven theorems.
The hallmark of a theorem is its universality; once proven, it holds true under specified conditions. Unlike conjectures or hypotheses, theorems are not subject to falsification; they withstand scrutiny and become integral to mathematical understanding. The process of proving theorems contributes to the robustness and reliability of mathematical theories, forming a foundation for further exploration and discovery within the discipline.
Hence, option D is correct.