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This

#+STARTUP: entitiespretty

in my org mode buffer allows Latex/MathJax symbols to render in situ . . . almost. I type, e.g., $\le$ and instantly the markup is replaced by the actual symbol. There are some symbols, however, that don't render -- although they do appear as expected in an export. This isn't a huge problem, but why does the buffer balk on, say, `$\bot$) or $\mapsto$?

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Because they don't exist in the tables org-entities or org-entities-user. You can customize the latter and add them if you want.

You need to figure out what to replace it with for LaTeX, HTML, ASCII, Latin1 and UTF8. Here's a possible definition for \bot although the Latin1 part could probably be improved:

#+begin_src emacs-lisp
  (add-to-list 'org-entities-user
             '("bot" "\\bot" t "⊥" "_|_" "_|_" "⊥"))
#+end_src

The doc for the variable says:

User-defined entities used in Org to produce special characters.
Each entry in this list is a list of strings.  It associates the name
of the entity that can be inserted into an Org file as \name with the
appropriate replacements for the different export backends.  The order
of the fields is the following

name                 As a string, without the leading backslash.
LaTeX replacement    In ready LaTeX, no further processing will take place.
LaTeX mathp          Either t or nil.  When t this entity needs to be in
                     math mode.
HTML replacement     In ready HTML, no further processing will take place.
                     Usually this will be an &...; entity.
ASCII replacement    Plain ASCII, no extensions.
Latin1 replacement   Use the special characters available in latin1.
utf-8 replacement    Use the special characters available in utf-8.

If you define new entities here that require specific LaTeX
packages to be loaded, add these packages to ‘org-latex-packages-alist’.

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