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What does the term 'mathematical induction' refer to?

Practice Questions

Q1
What does the term 'mathematical induction' refer to?
  1. A method for proving statements about natural numbers
  2. A technique for solving differential equations
  3. A principle in geometry
  4. A statistical inference method

Questions & Step-by-Step Solutions

What does the term 'mathematical induction' refer to?
  • Step 1: Understand that mathematical induction is a way to prove something is true for all natural numbers (like 1, 2, 3, ...).
  • Step 2: The process starts by proving the statement is true for the first natural number, usually 1.
  • Step 3: Next, assume the statement is true for some natural number 'k'. This is called the 'induction hypothesis'.
  • Step 4: Then, prove that if the statement is true for 'k', it must also be true for 'k + 1'.
  • Step 5: If both steps 2 and 4 are completed, you can conclude that the statement is true for all natural numbers.
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