mathematical induction

American  

noun

1. induction.

---

mathematical induction Cultural  

1. A method of proof in which a statement is proved for one step in a process, and it is shown that if the statement holds for that step, it holds for the next.

---

Etymology

Origin of mathematical induction

First recorded in 1830–40

Example Sentences

Therefore, the program is sound by the principle of mathematical induction.

From New York Times • Apr. 17, 2018

To all such numbers, proofs by mathematical induction can be validly applied.

From Our Knowledge of the External World as a Field for Scientific Method in Philosophy by Russell, Bertrand

This, in an elementary treatment of the subject, must be regarded as axiomatic; but it is really a simple case of mathematical induction.

From Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5 "Arculf" to "Armour, Philip" by Various

The property of being increased by the addition of 1—i.e. the property of non-reflexiveness—may serve to illustrate the limitations of mathematical induction.

From Our Knowledge of the External World as a Field for Scientific Method in Philosophy by Russell, Bertrand

To this inevitable induction of Dr. Harvey we are all driven in the end, by those intuitive processes of reasoning which are hardly less conclusive than mathematical induction itself.

From Life: Its True Genesis by Wright, R. W.