If and only if you made use of the divergent series or integral in a logically correct manner.mhill said:if we can proof an statement but we make use of a divergent series or integral to proof it.. would it be considered valid ??
A proof based on divergent series is a mathematical concept that involves using infinite series, or sums of infinitely many numbers, to prove a mathematical statement or theorem.
Unlike other types of proofs, a proof based on divergent series does not require the series to converge, meaning that the sum of the numbers in the series does not approach a finite value. Instead, it uses the properties of divergent series to prove a statement.
One example is the proof of the Euler-Mascheroni constant, which is a mathematical constant that arises in many areas of mathematics. The proof uses the harmonic series, which is a well-known example of a divergent series, to show that the Euler-Mascheroni constant exists and has a specific value.
Proofs based on divergent series have applications in various areas of mathematics, including number theory, analysis, and probability. They can also be used to solve problems in physics and engineering.
No, a proof based on divergent series, like any other mathematical proof, must be carefully constructed and rigorously checked to ensure its validity. It must also be backed up by sound mathematical reasoning and logic.