##  [Betti Number](/betti-number) 

  ##  [Betti Number](https://mathlogic.quantumdictionary.io/betti-number-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 & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A nonnegative integer equal to the rank of a homology group in a given dimension; it counts independent k-dimensional cycles modulo boundaries (the rank over Z or over a chosen coefficient field).

 

 

 

 

 





 

 



 ##  [Betti Number](https://algebra.quantumdictionary.io/betti-number-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A numerical invariant equal to the rank (dimension over a field) of a homology or cohomology group in a given degree, or equivalently the rank of a free module appearing in a minimal resolution; it counts independent cycles or relations in that degree.