A proof or demonstration is said to be rigorous if the validity of each step and the connections between the steps is explicitly made clear in such a way that the result follows with certainty. "Rigorous" proofs often rely on the postulates and results of formal systems that are themselves considered rigorous under stated conditions.
Rigorous
See also
Conclusion, Conjecture, Experimental Mathematics, ProofExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Rigorous." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Rigorous.html