#### Thesis Title

Differentiability, Continuity, and Existence of Limits

#### Date of Graduation

Fall 1994

#### Degree

Master of Science in Mathematics

#### Department

Mathematics

#### Committee Chair

Xingping Sun

#### Subject Categories

Mathematics

#### Abstract

In this thesis, we first demonstrate in various aspects the existence of everywhere continuous nowhere differentiable functions. We then address the question: could there exist a function defined on R that has a limit at each point of R, but fails to be continuous at any point? We show that the answer to this question is "No", and we establish the stronger result that if a function defined on the interval [a,b] has a limit at each point of a dense subset of [a,b], then the set of points where the function is continuous is dense, uncountable, and has the same cardinality as R.

#### Copyright

© Julie Ann Millett

#### Recommended Citation

Millett, Julie Ann, "Differentiability, Continuity, and Existence of Limits" (1994). *MSU Graduate Theses*. 860.

http://bearworks.missouristate.edu/theses/860

Citation-only

**Dissertation/Thesis**