Induction prove is a mathematical method used to prove statements or equations that hold true for all natural numbers. In the case of making fractions 1/2 to 1, induction prove can be used to show that the statement "all fractions between 1/2 and 1 can be made by adding 1/2 to itself" holds true for all natural numbers.
The first step is to prove that the statement holds true for the first natural number, which is 1 in this case. This can be done by showing that 1/2 can be made by adding 1/2 to itself.
The next step is to assume that the statement holds true for a certain natural number, n. This is called the "inductive hypothesis." In this case, we assume that all fractions between 1/2 and 1 can be made by adding 1/2 to itself n times.
Using the inductive hypothesis, we can show that the statement holds true for the next natural number, n+1. This is done by adding 1/2 to itself n+1 times, which is the same as adding 1/2 to itself n times and then adding 1/2 one more time. This proves that the statement holds true for n+1, and by the principle of mathematical induction, it holds true for all natural numbers.
Using induction prove allows us to prove a statement for an infinite set of numbers, in this case all natural numbers. This method is widely used in mathematics to prove statements and equations for all natural numbers, which would be impossible to do individually for each number.