 ##  [Well-Founded Induction](/well-founded-induction) 

  ##  [Well-Founded Induction](https://mathlogic.quantumdictionary.io/well-founded-induction-0) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

The principle that if a relation R on a set is well-founded (there are no infinite descending R-chains), and whenever an element x has the property provided all R-smaller elements do, then every element has that property; it generalizes ordinary induction on the naturals to arbitrary well-founded orders.