Which of the following best defines 'mathematical induction'?

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Question: Which of the following best defines \'mathematical induction\'?

Options:

Correct Answer: A method for proving statements for all natural numbers

Solution:

Mathematical induction is a proof technique used to establish that a statement holds for all natural numbers.

Which of the following best defines 'mathematical induction'?

Which of the following best defines 'mathematical induction'?

Step 1: Understand that mathematical induction is a method used in mathematics.
Step 2: Know that it is used to prove statements about natural numbers (like 1, 2, 3, ...).
Step 3: Realize that the process involves two main parts: the base case and the inductive step.
Step 4: The base case shows that the statement is true for the first natural number (usually 1).
Step 5: The inductive step shows that if the statement is true for one natural number, it must also be true for the next one.
Step 6: By completing these two steps, we can conclude that the statement is true for all natural numbers.

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