Not an answer, but here is a tip, given by A.J. Hildebrand, on using one letter macros:
Avoid one letter macros
Many one letter sequences have predefined meanings and thus cause conflicts if you try to use them for your own macros. Most of these one-letter macros are part of the TeX core, and usually not documented in Latex books. Thus, if a macro isn't listed in the index of a Latex book, it doesn't mean that it is not in use. To be certain that a macro isn't in use, you would have to check the original Knuth TeXbook, in addition to a comprehensive Latex reference.
You can largely avoid running into such problems by using at least two letters for a macro name. While there exist a few (non-obvious) two letter sequences that have predefined meanings (e.g., \aa), those are quite rare and the vast majority of two letter sequences are available as macro names. For example, to define \mathbf{v}, use \vv, or \bv (for "bold v"), rather than \v. The latter, \v, is predefined, whereas both \vv and \bv are available.
His website offers many more other useful tips for LaTeX, one can go over them if interested.
\newcommand\1{2}
...\newcommand{\2}{\frac{1}{2}}
? AFAIUnderstood the TeX macro processor is not able to read number characters in macro names, assuming they have their default catcode. It should be something like\expandafter\def\csname 2\endcsname{\frac{1}{2}}
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