Which one is correct? "mathematical induction" vs "the mathematical induction"? It's as often with the article as it is without so is it optional? Can either be used? Is there a difference?

Example 1: "Use (the) mathematical induction to prove the formula for the sum of a geometric series."

Example 2: "Chemistry students don't learn about (the) mathematical induction at the university.

Google the following using double quotes:

"Use the mathematical induction to prove the formula". 2 Results

"Use mathematical induction to prove the formula". 10200 Results

"learn about the mathematical induction". 0 results

"learn about mathematical induction". 27200 Results

So it's settled.


1 Answer 1


The term “mathematical induction” is used (grammatically) in the same way as mathematical operations such as addition and subtraction. You can use the more common/familiar terms to guide your intuition on this.

When speaking about applying the technique, the definite article is typically not used.

  • Prove the theorem by addition.

  • Prove the theorem by (no article) mathematical induction.

  • Learn about addition.

  • Learn about (no article) mathematical induction.

When referencing an instance of the technique, you might sometimes use an article to indicate that you are talking about that specific instance.

  • The addition used to prove the theorem involves the variable x.
  • The mathematical induction used to prove the theorem involves the variable x.

The difference is whether you are referring to the technique/concept or a concrete instance of its application. More generally, mathematical induction is a noun phrase consisting of a head noun that specifies an operation of some sort (induction) and a modifier (mathematical), and follows the usual conventions regarding article usage common to such constructs.

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.