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TheOtherDave comments on Open Thread: December 2011 - Less Wrong Discussion
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I generally say "triple-hat" to myself when I read it.
3↑↑↑3. The use of ^ instead is a limitation of ASCII.
Knuth called it the "triple-arrow" operator. I don't see any conjugations necessary, so "three triple-arrow three".
"Three pentated by three" also works.