math - What does the O(1) in "ln ln n / ln 2 + O(1)" mean? -

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i have difficulty understand o(1) notation in formula, stand constant? why people use big-o notation this?

formula

this formula comes paper "balanced allocations" azar et al., , formulas used in abstract:

abstract

here, term o(1) means "some term o(1)," meaning term n goes infinity bounded above constant. example, might 137, or sin n, or 1 / n2. value described therefore might ln ln n / ln 2 + 137, or ln ln n / ln 2 + sin n, etc.

this use of big-o notation common in formal mathematics when discussing low order terms in formula contribute small amount overall total. authors have written entire expression o(ln ln n), less precise ln ln n / ln 2 + o(1) because obscures fact coefficient on ln ln n 1 / ln 2 , low-order growth term bounded above constant. explicitly writing out " + o(1)", authors able give better precision.

hope helps!


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