Several invalid formulas

[aleksas]

Not all wxamples from https://en.wikibooks.org/wiki/LaTeX/Mathematics are valid.

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\alpha, \Alpha, \beta, \Beta, \gamma, \Gamma, \pi, \Pi, \phi, \varphi, \mu, \Phi

ERR: Undefined control sequence \Alpha (also \Beta)

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\frac{n!}{k!(n-k)!} = \binom{n}{k}

ERR: Undefined control sequence \binom

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3\times\sfrac{1}{2}=1\sfrac{1}{2}

ERR: 3\times\sfrac{1}{2}=1\sfrac{1}{2}

\begin{equation} x = a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cfrac{1}{a_3 + \cfrac{1}{a_4} } } } \end{equation}

ERR: Undefined control sequence \cfrac

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\sum_{\substack{ 0<i<m \ 0<j<n }} P(i,j)

ERR: Undefined control sequence \substack

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( a ), [ b ], { c }, | d |, | e |, \langle f \rangle, \lfloor g \rfloor, \lceil h \rceil, \ulcorner i \urcorner

ERR: Undefined control sequence \ulcorner

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[ \begin{matrix} a & b & c \ d & e & f \ g & h & i \end{matrix} ] ERR: Small brackets and [ causes err