Journal of Prime Research in Mathematics

# On A Mathematical Contradiction to Rethink Associativity and Commutativity for Infinite Series and Infinite Products

Md. Shafiqul Islam $$^{a,*}$$, Sumit Bhowmick $$^a$$
$$^a$$ Department of Materials and Metallurgical Engineering, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladesh.
Correspondence should be addressed to: shafiqmme@gmail.com

### Abstract

This paper deals with two contradictory values of π, focusing on the invalidity of associative and commutative laws for infinite series. The argument shows that operating with some infinite products leads to some dangerous contradictions such as the π value turns out to be 4 or 8/3. The study and the findings embedded with the article’s methodology points out that these classical operations like associativity and commutativity on infinite series or infinite products must be handled carefully.

#### Keywords:

Infinite Series, Infinite Product, Commutative Law.