#### Theorem 30.1 (Cauchy). First Theorem.

No statement.

This section demonstrates the numbering patterns used throughout PreTeXt. There are five subsections. Two intermediate subsections each have two subsubsections. This creates a total of seven divisions that are leaves of the document tree. In each leaf we have placed two numbered theorems, for a total of fourteen. There is no real content, this is just a demonstration.

Use values of

`0`

through `3`

for the `numbering.theorems.level`

parameter to see how these numbers change accordingly. It is easiest to compare if you use `chunk.level < 2`

so the theorems all land on the same page if you are previewing in HTML.A document leaf.

No statement.

No statement.

Further subdivided.

A document leaf.

No statement.

No statement.

A document leaf.

No statement.

No statement.

A document leaf.

No statement.

No statement.

Further subdivided. We include two theorems as numbered items in the introduction to test their numbers, which should always be logical.

No statement.

No statement.

A document leaf.

No statement.

No statement.

A document leaf.

No statement.

No statement.

Conclusion now. We include two theorems as numbered items in the conclusion to test their numbers, which are sometimes totally illogical and are inconsistent across output formats. To see the effect, set the level for numbering theorems to ^{ 1 }

for details.

`3`

. See this GitHub Issue #139`github.com/PreTeXtBook/pretext/issues/139`

No statement.

No statement.

A document leaf.

No statement.

No statement.

We have a lot of theorems in this section, so we illustrate including an automatic list of these here. We use the

`elements`

attribute to limit the list to `theorem`

elements, and we use the `scope`

attribute to limit the list to this `section`

. You can use an introductory `p`

like this one, or not. The list gets no title or visual separation, so use the usual subdivision elements to make that happen. The `elements`

attribute can be a space-delimited list of many different elements. This list should not include the Fundamental Theorem of Calculus, Theorem 2.1. See a slightly different example in Appendix F.
Theorem 30.1 First Theorem

Theorem 30.2 Second Theorem

Theorem 30.3 First Theorem!

Theorem 30.4 Second Theorem?

Theorem 30.5 First Theorem?

Theorem 30.6 Second Theorem!

Theorem 30.7 First Theorem

Theorem 30.8 Second Theorem

Theorem 30.9 Good Numbered Theorem One

Theorem 30.10 Good Numbered Theorem Two

Theorem 30.11 First Theorem

Theorem 30.12 Second Theorem

Theorem 30.13 First Theorem

Theorem 30.14 Second Theorem

Theorem 30.15 Bad Numbered Theorem One

Theorem 30.16 Bad Numbered Theorem Two

Theorem 30.17 First Theorem

Theorem 30.18 Second Theorem

LaTeX has trouble with brackets that end up inside optional arguments, so this subsection title is only a check on the defense against that. And now an

`<exercise>`

with a title that could really be a problem.The right brace is is used as a grouping character in LaTeX so this is just a test of its behavior in titles.

A faux hint to get this exercise to migrate into a

`<solutions>`

.And now a right brace in a division title.

And now a right bracket within math in a division title.

We do not test a right brace within math, since it should be escaped, as is normal LaTeX practice.

This exercise is here just as a test of the

`<solutions>`

division coming next. So it is serving a purpose, even if it is not apparent.A hint, so this exercise looks identical in structure to the one in the previous subsection.

This is a

`<solutions>`

division, which will be a peer of the other `<subsection>`

in this `<section>`

. The default behavior is to look to the parent division (a `<section>`

here) and collect all the hints, answers, and solutions from every `<exercise>`

(and friends) inside this containing division. (There are just two, similar inline `<exercise>`

.)But instead of the default, we employ a *define* the parent division of the exercises whose solutions will be shown. In this example we specify the

`@scope`

attribute to `<subsection>`

that is two back, the one which tests brackets in titles.A faux hint to get this exercise to migrate into a

`<solutions>`

.