The principle of strong mathematical induction is to prove that a series of mathematical statements containing integers is true. In order to do this one must prove that the first sequence in the statement is true. Then they must use this to demonstrate that any other given statement within the series is also true; therefore proving that the entire series is true even if it were to be infinite.
The method can be applied for a variety of mathematical equations in order to find the absolute truth of the series of statements. However - it is not the same as inductive reasoning. Inductive reasoning is not far less mathematical and consists more of logical analysis.
The method dates all the way back to 370 BC when it is believed that the Greek mathematician Plato first documented mathematical induction. In fact - the earliest reported origin of mathematical induction was found when another Greek mathematician - known as Euclid - used it to prove that prime numbers were infinite.
Perhaps the best metaphor to further describe this method would be to imagine a never-ending run of dominoes, all stacked up next to one another. The mathematical induction that you are looking to form would prove that this run of dominoes would endlessly continue to fall when toppled. You are looking to prove that the pattern continues. As well as that, you would be looking to prove that even if you didn't push over the first few dominoes and skipped further down the line, they would still continue to fall infinitely.
The method can be applied for a variety of mathematical equations in order to find the absolute truth of the series of statements. However - it is not the same as inductive reasoning. Inductive reasoning is not far less mathematical and consists more of logical analysis.
- The history of the method
The method dates all the way back to 370 BC when it is believed that the Greek mathematician Plato first documented mathematical induction. In fact - the earliest reported origin of mathematical induction was found when another Greek mathematician - known as Euclid - used it to prove that prime numbers were infinite.
- Metaphorically speaking
Perhaps the best metaphor to further describe this method would be to imagine a never-ending run of dominoes, all stacked up next to one another. The mathematical induction that you are looking to form would prove that this run of dominoes would endlessly continue to fall when toppled. You are looking to prove that the pattern continues. As well as that, you would be looking to prove that even if you didn't push over the first few dominoes and skipped further down the line, they would still continue to fall infinitely.
