What is discontinuous width point when using width tool in illustrator

Question

I am currently reading the book Adobe Illustrator Classroom in a Book (2020 release)

In the lesson 4, Width tool section(page 463) author has mentioned following about discontinious width point :-

You can drag one width point on top of another width point to create a discontinuous width point. If you double-click a discontinuous width point, the Width Point Edit dialog box allows you to edit both width points.

However I didn't understand this at all, I think the whole purpose of width tool is to increase the width of stroke at certain point.

(a) Why would somebody drop the one width point on the top of another ?
(b) What would be archived by doing so ?
(c) What is discontinuous width point ?

Answer 1

A) Why

So that you can have sharper alterations between width markers. Similar to having two gradient stops on top of each other. The transition between width markers is reduced to zero, essentially allowing for hard, sharp, edges within the curves the markers create.

B) What

See A.

C) Discontinuous

For most humans, Webster defines discontinuous as: having gaps or spaces.

However, Adobe devs are engineers. In mathematics, a discontinuous curve is one which is not a continuous or "smooth" curve. A curve which would require you to lift a pencil and reposition if you were to try and draw the curve manually.

So, in this instance, "discontinuous" refers to an area along the path where Width markers create an un-smooth curve (see image above)

Unfortunately, because the usage of "discontinuous" is referring more to mathematics than traditional language, there may be other areas where Adobe anticipates the usage of "discontinuous" in a similar manner. i.e. ACE tests.

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All this is based solely on the question. I did not actually review that section of the Illustrator Classroom in a Book. It can be helpful to remember that engineers write the documentation.

It is helpful to always refer to mathematics or engineering usage first when seeking term definitions for technical aspects of Illustrator.