Let us study about mathematical induction,
Mathematical induction, or proof by induction, is a method of mathematical proof typically used to establish that a given statement is true for all natural numbers. It can also be used in more general settings as will be described below. An induction variant is used in computer science to prove that expressions which can be evaluated are equivalent, and this is known as structural induction.
The simplest and most common form of mathematical induction proves that a statement holds for all natural numbers n and consists of two steps:
Showing that the statement holds when n = 0.
Showing that if the statement holds for n = m, then the same statement also holds for n = m + 1.
To understand why the two steps are in fact sufficient, it is helpful to think of the domino effect: if you have a long row of dominos standing on end and you can be sure that
The first domino will fall.
Whenever a domino falls, its next neighbor will also fall.
then you can conclude that all dominos will fall.
Hope the above explanation was helpful.
Mathematical induction, or proof by induction, is a method of mathematical proof typically used to establish that a given statement is true for all natural numbers. It can also be used in more general settings as will be described below. An induction variant is used in computer science to prove that expressions which can be evaluated are equivalent, and this is known as structural induction.
The simplest and most common form of mathematical induction proves that a statement holds for all natural numbers n and consists of two steps:
Showing that the statement holds when n = 0.
Showing that if the statement holds for n = m, then the same statement also holds for n = m + 1.
To understand why the two steps are in fact sufficient, it is helpful to think of the domino effect: if you have a long row of dominos standing on end and you can be sure that
The first domino will fall.
Whenever a domino falls, its next neighbor will also fall.
then you can conclude that all dominos will fall.
Hope the above explanation was helpful.
