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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.

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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.

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