Suppose we want some MathML like this:
<?xml version="1.0" encoding="UTF-8"?>
<mathml:math xmlns:mathml="http://www.w3.org/1998/Math/MathML">
  <mathml:mrow>
    <mathml:mi>f(0)</mathml:mi>
    <mathml:mo>=</mathml:mo>
    <mathml:mn>0</mathml:mn>
  </mathml:mrow>
  <mathml:mrow>
    <mathml:mi>f(1)</mathml:mi>
    <mathml:mo>=</mathml:mo>
    <mathml:mn>1</mathml:mn>
  </mathml:mrow>
  <mathml:mrow>
    <mathml:mi>f(2)</mathml:mi>
    <mathml:mo>=</mathml:mo>
    <mathml:mn>1</mathml:mn>
  </mathml:mrow>
</mathml:math>
Do not use the qualified names like mathml:mn.
Instead use the prefixes mathml, local names like mn,
and URIs like http://www.w3.org/1998/Math/MathML
to create the elements.
Do not include xmlns attributes 
like xmlns:mathml="http://www.w3.org/1998/Math/MathML".
XMLOutputter will
decide where to put the xmlns attributes 
when the document is serialized.