What Is a Limit of a Function? A 5 Minute Introduction

[Greg Bernhardt]

Table of Contents
ToggleWhat is a limit?What is a function?
Definition of a Limit of  a FunctionEquationsExtended explanation
What is a limit?
In mathematics, a limit is a fundamental concept used to describe the behavior of a function or sequence as it approaches a particular point or value. Limits play a crucial role in calculus, where they are used to define concepts like continuity, derivatives, and integrals.
Here are key aspects of limits:

Definition: The limit of a function or...

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[fresh_42]

This has not to be confused with limits of sequences of functions as considered in functional analysis, e.g. example 5.9. in https://www.physicsforums.com/insights/hilbert-spaces-relatives/

 

[guhag]

Hi Greg. I am trying to develop the skill of "proofs based reasoning". I am a synthetic organic chemist, and would love to learn the math associated with chemistry, for example: Linear algebra, Group theory (Quantum chem). I would also like to learn to write, analyze and appreciate proofs in Analysis, for instance to read and work out problems in Apostol, Spivak.

I don't have any agenda/timelines (except in this lifetime, that'd be good!) and just would like to do it for self-satisfaction. I tried reading "Intro to logic" , truth tables (If p then q,) but I fail to see the jump from those to, say, delta-epsilon limits proof.

Maybe this is all silly... but in case it is not, would you be able to suggest/point out how I could go about this? Thanks and appreciate your time and help.