With only the TeX fonts installed IE8 cannot render double-struck characters from the Letterlike Symbols area (U+2100 - U+214F), while double-strucks addressed by attribute mathvariant="double-struck" (e.g. <mi mathvariant="double-struck">K</mi>) render OK.
Examples for rendering failures:
<mi>ℤ</mi>
<mi>ℕ</mi>
<mi>ℙ</mi>
Other browsers (FF, Opera) dont bother at all and can display both ways.
You are right, the MathJax TeX fonts don't currently include those characters at those locations (the font data should be modified to remap them to the locations where those glyphs do appear, and I will look into fixing that).
The reason it works in other browsers is that they are finding the characters in OTHER fonts automatically (not in the MathJax TeX fonts), but IE doesn't do that (it only looks in one font, and if not there, gives up looking).
Davide
A possible solution would be to map all those historical double-struck remainders in the U+2100 area for output to real double-strucks, like:
<mi>ℂ</mi> -> <mi mathvariant="double-struck">C</mi>
<mi>ℍ</mi> -> <mi mathvariant="double-struck">H</mi>
<mi>ℕ</mi> -> <mi mathvariant="double-struck">N</mi>
<mi>ℙ</mi> -> <mi mathvariant="double-struck">P</mi>
<mi>ℚ</mi> -> <mi mathvariant="double-struck">Q</mi>
<mi>ℝ</mi> -> <mi mathvariant="double-struck">R</mi>
<mi>ℤ</mi> -> <mi mathvariant="double-struck">Z</mi>
<mi>ⅅ</mi> -> <mi mathvariant="double-struck">D</mi>
Would that be a) possible and b) a good solution ?
Yes, when I said "the font data should be modified to remap them to the locations where those glyphs do appear" that is the sort of thing I had in mind.
Davide
OK, great.
Another observation somehow connected to this issue is: MathJax renders all double-struck <mi>s by default in italics. I firmly believe this is wrong, regardless what the MathML spec is saying about rendering single letter <mi> elements. Maybe by the notion of a "single letter" they did not include the idea of a double struck letter.
Anyway, native MathML rendering on Firefox for these letters always is upright, i.e. normal, if you look to Wikipedia e.g. http://en.wikipedia.org/wiki/Countable_set its all upright, and I never saw anything different than upright in any text book if have read.