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This questions looks a bit stupid. But I am confused on a statement which says that the value of some xyz parameter is expected to be of order 1. Does it mean that its value is less than $10^1$ or its value is less than 1?

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Some people would answer this something like:

$$O(x) = 10^{\operatorname{round}( \log_{10} x)} $$

This puts the break-points at about $3\times 10^n$, e.g. $O(1)$ is between $0.3$ and $3$, but these are not hard and fast limits -- e.g. I wouldn't balk if an $O(1)$ number came out up around even 10 (or 0.1).

I've often seen "the parameter is $O(1)$" in terms of geometric constants, $2 \pi$, $4\pi/3$, $\sqrt{2}$, $\sqrt{3}/2 \ldots$ (and their inverses) that arise from basic geometrical shapes, and these can be outside the pedantic limits, but still are conventionally described as $O(1)$.

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  • $\begingroup$ I've deleted some comments relating to the previous version of the post. $\endgroup$ – David Z Jul 18 '17 at 0:53

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