Limit and Continuity Revisited via Convergence
Jitender Singh *
Department of Mathematics, Guru Nanak Dev University, Amritsar-143005, India.
Harpreet K. Grover
Department of Mathematics, Guru Nanak Dev University, Amritsar-143005, India.
*Author to whom correspondence should be addressed.
Abstract
We derive some of the standard results on limits of elementary functions defined on subsets of real-line, whose rigorous proofs are often avoided in the routine teaching and learning of calculus. For proofs, we essentially follow the Weierstrass's systematized modern formalization of Cauchy's idea of transforming the concept of limit into "the algebra of inequalities".
Keywords: Limit, continuity, convergence, calculus