## Date of Submission

Spring 2016

## Academic Programs and Concentrations

Mathematics

## Project Advisor 1

Japheth Wood

## Abstract/Artist's Statement

It is known that there is an agreed upon convention of how to go about evaluating expressions in the real numbers. We colloquially call this PEMDAS, which is short for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It is also called the Order of Operations, since it is the order in which we execute the operators of a given expression. When we remove this convention and begin to execute the operators in every possible order, we begin to see that this allows for many different values based on the order in which the operations are executed. We will investigate this question by looking at how this affects the operations on the real numbers through using parentheses to force operators to be executed in a specific order. We compute the asymptotic bound for the number of outcomes, defined as associativity, for each of the operations on the real numbers.

## Access Agreement

Open Access

## Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.

## Recommended Citation

Audino, Samuel Joseph, "Associativity of Binary Operations on the Real Numbers" (2016). *Senior Projects Spring 2016*. 179.

https://digitalcommons.bard.edu/senproj_s2016/179

This work is protected by a Creative Commons license. Any use not permitted under that license is prohibited.