Wrong example of nested <ul> <li> on very well known web design tutorial site

Question

http://www.webdesignfromscratch.com/html-css/html-lists.php on this page's example of nested Unordered lists <ul> list's code is not validating on W3C validation

this is a code of this page http://www.webdesignfromscratch.com/html-css/html-lists.php

<ul>
  <li>Item one</li>
  <li>Item two</li>
  <li>Watch, you can easily nest list items: This item has some sub-items</li>
  <ul>
    <li>Sub-item one</li>
    <li>Sub-item two</li>
    <li>Shall we do a 3rd nested list?</li>
    <ul>
      <li>OK</li>
      <li>Your browser should automatically use different bullet styles for each level.</li>
    </ul>
  </ul>
</ul>

website owner should test code validity before and after writing code

Answer 1

The nested <ul> should be inside the <li>.

Answer 2

Because due to XHTML (and probably also due to HTML 4), nested <ul> must be a child of <li>

Example:

<ul>
  <li> Here is level 1
    <ul>
      <li> Bla bla (level 2) </li>
    </ul>
  </li>
</ul>

looks like:

• Here is level 1
  • Bla bla (level 2)

Edit: link: http://www.w3schools.com/XHTML/xhtml_html.asp
Edit: prepared spec for html5: http://www.w3.org/MarkUp/html-spec/html-spec_5.html#SEC5.6 also shows how to make nesting valid

Answer 3

Your sub-list(s) must be enclosed in a li tag.

i.e.

<ul>
  <li>Item one</li>
  <li>Item two</li>
  <li>Watch, you can easily nest list items: This item has some sub-items
  <ul>
    <li>Sub-item one</li>
    <li>Sub-item two</li>
    <li>Shall we do a 3rd nested list?
    <ul>
      <li>OK</li>
      <li>Your browser should automatically use different bullet styles for each level.</li>
    </ul></li>
  </ul></li>
</ul>