Mathematical induction.
Definition.
Mathematical induction is a technique in mathematics used in proving a formula, theorem or formula of each natural number is true. There are two steps involved in the method. The first step known as the base step, shows that a statement is correct for each first number while the second step also known as the inductive step, demonstrates that if the nth iteration is true, then (n+1)th iteration is also correct.
Demonstration
First step- An initial number should be considered whereby the statement should be true. The illustration, n=initial number, should be true. Don't use plagiarised sources.Get your custom essay just from $11/page
Second step-Any number showing n=k , should be assumed to be a true statement. Then n=k+1 statement should also be proved to be true. The statement, n=k+1 is broken into two. The first part, n=1, is already proved. Therefore, we are just required to prove the other part (Hummel & Kenneth, 2018).
Importance of Mathematical Induction.
Generally, mathematical induction is essential in proving that the statements for all natural values are true. As we have seen above, the first step shows that the declaration in the question is correct for the first number. So if it proves that the declaration of one value is true, the other value should also be true(Rosenthal et al., 2018)
Limitations of Mathematical induction.
Mathematical induction cannot be used in solving continuous mathematical problems. It is also considered to be complicated in some cases (Golovina & Yaglom, 2019).
It is still a wonder how mathematical induction proves that all statements are true.
.
Golovina, L. I., & Yaglom, I. M. (2019). Induction in geometry. Courier Dover Publications.
Hummel, Kenneth E. “Mathematical Induction.” In Introductory Concepts for Abstract Mathematics, pp. 91-102. Chapman and Hall/CRC, 2018.
Rosenthal, D., Rosenthal, D., & Rosenthal, P. (2018). Mathematical Induction. In A Readable Introduction to Real Mathematics (pp. 9-22). Springer, Cham.