#### Document Type

Article

#### Publication Date

1-1-2018

#### Publication Source

Proceedings of the 2017 Undergraduate Mathematics Day

#### Inclusive pages

11-16

#### Abstract

In February 2017, a number theoretic problem was posed in Mathematics Magazine by Souvik Dey, a master’s student in India. The problem asked whether it was possible to represent a real number by a finite sum of elements in an open subset of the real numbers that contained one positive and one negative number. This paper not only provides a solutionto the original problem, but proves an analogous statement for elements of R2.

#### Keywords

Spanning Sets

#### Disciplines

Mathematics

#### eCommons Citation

Dominguez, Lewis T. and Bouchat, Rachelle R., "Finite Sum Representations of Elements in R and R2" (2018). *Proceedings of Undergraduate Mathematics Day*. 31.

https://ecommons.udayton.edu/mth_epumd/31

## Comments

This paper was presented Saturday, Nov. 11, 2017, as part of Undergraduate Mathematics Day at the University of Dayton. Launched in 2003, Undergraduate Mathematics Day is held in odd-numbered years and alternates with the Biennial Alumni Career Seminar. The conference coincides with the annual Schraut Memorial Lecture, named Kenneth “Doc” Schraut, a mathematics faculty member from 1940 to 1978 and department chair from 1954 to 1970.

The 2017 invited lecturer was Joseph Gallian, the Morse Alumni Distinguished University Professor of Teaching at the University of Minnesota Duluth and a past president of the Mathematical Association of America. He presented the lecture “Breaking Driver’s License Codes.”