NotesFAQContact Us
Collection
Advanced
Search Tips
Publication Date
In 20252
Descriptor
Mathematical Logic2
Number Concepts2
Equations (Mathematics)1
Geometry1
Mathematical Concepts1
Mathematics1
Numbers1
Validity1
Source
International Journal of…2
Author
F. M. S. Lima1
Giovanni Vincenzi1
Publication Type
Journal Articles2
Reports - Descriptive2
Education Level
Audience
Location
Laws, Policies, & Programs
Assessments and Surveys
What Works Clearinghouse Rating
Showing all 2 results Save | Export
A Simpler Elementary Proof That "e" Is Irrational
Peer reviewed Peer reviewed
Direct linkDirect link
F. M. S. Lima – International Journal of Mathematical Education in Science and Technology, 2025
In this short note I present an elementary proof of irrationality for the number "e," the base of the natural logarithm. It is simpler than other known proofs as it does not use comparisons with geometric series, nor Beukers' integrals, and it does not assume that "e" is a rational number from the beginning.
Descriptors: Mathematical Logic, Number Concepts, Geometry, Equations (Mathematics)
Irrationality via Base-B Representation: An Alternative Proof of Gauss's Lemma
Peer reviewed Peer reviewed
Direct linkDirect link
Giovanni Vincenzi – International Journal of Mathematical Education in Science and Technology, 2025
Using the basic properties of the base-b representation of rational numbers, we will give an elementary proof of Gauss's lemma: "Every real root of a monic polynomial with integer coefficients is either an integer or irrational." The paper offers a new perspective in understanding the meaning of 'irrational numbers' from a deeper…
Descriptors: Mathematical Logic, Validity, Numbers, Mathematics