Cumulative misalignment in fractions in comments

Question

In this comment, the fraction $\frac{(2n+2)!}{(n+1)!}$ is misaligned. I repeated the same input in a second comment underneath the first, and the alignment gets even worse there. Here's a screenshot from my browser (Firefox $44.0.2$, Mac OS $10.5.5$):

Here's the input for the affected equation:

\binom{2n}n=\frac{(2n)!}{n!^2}=\frac{(n+1)^2}{(2n+1)(2n+2)}\frac{(2n+2)!}{(n+1)!‌​‌​}=\frac{(n+1)^2}{(2n+1)(2n+2)}\binom{2(n+1)}{n+1}

This is the only related question I could find; as far as I can tell, that was a different issue that was resolved.

Answer 1

There are several invisible characters in the input, and that is causing the unexpected alignment. The characters are U+200B (ZERO WIDTH SPACE) and U+200C (ZERO WIDTH NON-JOINER). These are the characters that the comment code inserts into long runs of characters that have no spaces. There several copies of them, so it may be that you edited the comment several times?

You can see the characters in the MathML output. If you use the MathJax contextual menu to Show Math As MathML (on the example in Jyrki's comment for example), then you should see

      ...
      <mn>2</mn>
      <mo stretchy="false">)</mo>
      <mo>!</mo>
    </mrow>
    <mrow>
      <mo stretchy="false">(</mo>
      <mi>n</mi>
      <mo>+</mo>
      <mn>1</mn>
      <mo>&#x200C;</mo>
      <mo>&#x200B;</mo>
      <mo stretchy="false">)</mo>
      <mo>!</mo>
      <mo>&#x200C;</mo>
      <mo>&#x200B;</mo>
      <mo>&#x200C;</mo>
      <mo>&#x200B;</mo>
    </mrow>
  </mfrac>
  <mo>=</mo>
  <mfrac>
  ...

where you can see the ‌ and ​ in several places. These are throwing off the width of the denominator.

Answer 2

A strange thing. In case it helps tracing the problem here's what it looks like if you insert a \qquad in front of the offending denominator. Posting this as an answer instead of a comment so that A) anyone so inclined can tinker with it more, B) the output won't be disturbed by the known 80-character feature preventing parsing of long TeX-snippets inside a comment.

Code snippet/output pairs follow

\binom{2n}n=\frac{(2n)!}{n!^2}=\frac{(n+1)^2}{(2n+1)(2n+2)}\frac{(2n+2)!}{\qquad(n+1)!} =\frac{(n+1)^2}{(2n+1)(2n+2)}\binom{2(n+1)}{n+1} $$ \binom{2n}n=\frac{(2n)!}{n!^2}=\frac{(n+1)^2}{(2n+1)(2n+2)}\frac{(2n+2)!}{\qquad(n+1)!} =\frac{(n+1)^2}{(2n+1)(2n+2)}\binom{2(n+1)}{n+1}$$

\binom{2n}n=\frac{(2n)!}{n!^2}=\frac{(n+1)^2}{(2n+1)(2n+2)} \frac{(2n+2)!}{\qquad(n+1)​‌​!}=\frac{(n+1)^2}{(2n+1)(2n+2)}\binom{2(n+1)}{n+1} $$ \binom{2n}n=\frac{(2n)!}{n!^2}=\frac{(n+1)^2}{(2n+1)(2n+2)} \frac{(2n+2)!}{\qquad(n+1)!​‌​}=\frac{(n+1)^2}{(2n+1)(2n+2)}\binom{2(n+1)}{n+1}$$