I think the &quot;confusion&quot; is justified.  It&#x27;s a good thing(tm) to start with the concept of &quot;normal with respect to a base&quot; and then move on to say that &quot;normal&quot; or &quot;absolutely normal&quot; means &quot;normal for every base (greater than 1).&quot;<p>Wikipedia does this, adding the extra term &quot;simply normal&quot; for the case where we are talking about relative to a single base:<p><pre><code>    We say that x is simply normal in base b if
    the sequence S(x,b) is simply normal, and
    that x is normal in base b if the sequence
    S(x,b) is normal.  The number x is called a
    normal number (or sometimes an absolutely
    normal number) if it is normal in base b
    for every integer b greater than 1.
</code></pre>
For the purposes of explanation, especially to non-technical audiences, I think the approach taken is fully justified.<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Normal_number" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Normal_number</a>