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What's the best practice to typeset Knuth's up-Arrow notation?

\uparrow and \upuparrow are relation symbols (according to unimath-symbols.pdf). But in Knuth's up arrow notation, these should be a binary operator. So, how should on treat this difference?

Secondly, should double up arrows be typeset as \upuparrow or as \uparrow\uparrow, which illustrates the double nature better.

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For the first part, you could define a command using \mathbin,as in \newcommand\kuparrow{\mathbin{\uparrow}}. – Gonzalo Medina Apr 22 '13 at 19:20

There is a command \mathbin for creation of binary operators, so something like

$a\binuparrow b$


As to your second questions, tastes differ

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