in MES Science2 years ago

Several years ago I did an overview video on continuity and continuous functions but did not go through in too much detail so I have done just that in this video. In this video I go over what it means for a function to be continuous as well as illustrate several cases when a function is discontinuous or not continuous.

Watch video on:

Download video notes:!As32ynv0LoaIiMpD5-WiMmjTno4_-A?e=U3Wj68

View Video Notes Below!

Download these notes: Link is in video description.
View these notes as an article:
Subscribe via email:
Donate! :)
Buy MES merchandise!

Reuse of my videos:

  • Feel free to make use of / re-upload / monetize my videos as long as you provide a link to the original video.

Fight back against censorship:

  • Bookmark sites/channels/accounts and check periodically
  • Remember to always archive website pages in case they get deleted/changed.

Buy "Where Did The Towers Go?" by Dr. Judy Wood:
Subscribe to MES Truth:

Join my forums!

Follow along my epic video series:

NOTE #1: If you don't have time to watch this whole video:

Browser extension recommendations:



Mathematical definition of continuity corresponds closely with the meaning in everyday language

A continuous process is one that takes places gradually, without interruption or abrupt change.


A function f is continuous at a number a if:


This definition implicitly requires that:

  1. f(a) is defined (that is, a is in the domain of f)
  2. limx→a⁡ f(x) exists
  3. limx→a⁡ f(x) = f(a) exists

We say a function is discontinuous otherwise.


Discontinuous or not continuous cases

Case 1: f(a) is not defined


Case 2: limx→a⁡ f(x) does not exist


Case 3: limx→a⁡ f(x) ≠ f(a)