Thank you, Branodn and  Doug for quick reply!

The word "upper bound" is also used in Japan with mathematics.

> I think it means that the implementation of quick_ratio() is not defined in
> a lot of detail, except to say that the function will return a value that is
> an upper bound of the value returned by ratio().

That's the answer I wanted!!

I've got "This isn't defined beyond that" means
"This method is not defined in detail more than".

I've misread that "beyond" means "over the upper bound".
Maybe, "more" is easier than "beyond" for non-native English
readers.

Thank you very well.
-- 
INADA Naoki  <songofaca...@gmail.com>
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