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Reading the Comprehensive Latex Symbol List (30 November 2015), I find on page 29 that * corresponds to \ast - at least as a glyph. Which are the other non-backslash (mathematical) symbols which correspond to a backslash symbol name in Latex, and what do they correspond to? For example, I would expect +, - and / to have corresponding backslash-names.

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the don't by default, you can of course define command names if you wish. – David Carlisle Feb 15 at 21:13
    
So for example +, -, and / are their own symbols, not aliases? What would be a comprehensive list of all such non-backslash symbols? – Kaba Feb 15 at 21:29
    
* and \ast are not really aliases either, they are defined separately but with the same definition, one is not defined in terms of the other. every character in math mode is such a symbol so for example a is defined to come from the math italic font but 1 is defined to come from the upright roman font. – David Carlisle Feb 15 at 21:30
up vote 11 down vote accepted

The complete list should be

* \ast
[ \lbrack
] \rbrack
| \vert
= \Relbar

and you can maybe add

\{ \lbrace
\} \rbrace
   \backslash

Note that \mid produces the same symbol as | or \vert, but with the type “relation”; similarly \colon produces a colon, but with a different spacing from :.

There is also \slash, that produces / but with a line break allowed after it.

I'm not sure why \ast has been defined in plain TeX (possibly because Knuth sometimes needed * with a different meaning). The reason for \lbrack is for providing [ in a context where the latter cannot be used because it could be mistaken for the start of an optional argument; \rbrack is there for symmetry. For sure, Knuth needed | for his own purposes, so he provided \vert as an alias.

With amsmath the same symbol as | is produced by \lvert and \rvert, but with the types “opening” and “closing” respectively.

The reason for \Relbar is because the equals sign is used as extender for long double arrows; in some fonts a different symbol might be used, so \Relbar is by default defined as =, but can be redefined without the need to modify the definitions for \Longrightarrow and \Longleftarrow needn't be.

\lbrace and \rbrace are useful in order to fool smart editors that like to pair delimiters.

There is no alias for + and -, but they can be easily defined.

A reversed situation happens for < and \langle (and similarly for > and \rangle): the constructions \bigl< or \left< are shorthands for \bigl\langle and \left\langle, but < should never be used alone for denoting an angle bracket.

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@DavidCarlisle They're reversed: \left< is a synonym for \left\langle, but the symbol produced is not <. – egreg Feb 15 at 21:33

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