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Deposit #94

A Streaming Video

  Michael Krebs,  CSULA
Jamie Pommersheim, 
Reed College

The Definition of the Limit:  A Streaming Video

Definition of a Limit Video

   Stream the video here:

  Download the video here:

  We invite you to download this video to your laptop for use into the classroom.

Turn on your audio and be patient.  The speed of your internet connection makes a difference.
Note:  If your connection has problems streaming in RealOne Player, try downloading to the "mp4" format.
Windows Media Player version 8 or greater is recommended.  If not installed on your computer a free download is available.

A message to faculty:

We present a short video which may be used in a Calculus, Analysis, or History of Math.   After first discussing the historical development of the epsilon-delta definition, the video then briefly takes students through the underlying visual logic.

We wish to reassure faculty that we consider the video as only an initial introduction to a definition of the limit.  We leave it to the classroom professor to lead students in a precise discussion of rigor in the theory of limits.

"One magnitude is said to be the limit of another magnitude when the second may approach the first within any given magnitude, however small, though the second magnitude may never exceed the magnitude it approaches."

D'Alembert in his article on the term limit in the famous French Encyclopédie.

  • Spelling error: "Issac Newton" should be "Isaac Newton."
  • The precise quote from Berkeley is: "And what are these Fluxions . . . may we not call them the ghosts of departed quantities?"
  • Weierstrass (1815-1897), the "father of modern analysis," was working in the mid to late 1800's.  His  "ε - δ" terminology has become standard universal notation.
Weierstrass equations

Useful Links and Book
James Stewart, Calculus, 5th ed,. Thomson Brooks/Cole, 2003, p. 92.  Read "The Precise Definition of a Limit."
David M. Burton, The History of Mathematics, 6th ed., McGraw Hill, 2007, pp. 602-608.  Read "The Age of Rigor: D'Alembert and Cauchy on Limits."
Howard Eves, An Introduction to the History of Mathematics, 6th ed,. The Saunders College Publishing, 1990.
Victor J. Katz, A Brief History of Mathematics, BRIEF VERSION, Pearson Addison Wesley, 2004, p. 356; 432-433.

If you enjoyed the streaming video on Definition of the Limit,  we suggest you also view two other important calculus videos in the NCB.

Geometric Series - Convergence
     Robert Meyer  < >

Harmonic Series - Divergence
     Michael Krebs and Jeffrey L. Dergidge < >
Information Technology Services,
Taping and Editing by

Shirley Gray, Producer
William Stellmacher, Director

Dennis Kimura, Graphics
Yarimar RodasCordova, Video Editor