I was told that saying

A equals B within a factor C

is not correct. Is it true? My interlocutor, who is not a native anglophone, told me that "within" cannot be used in such a way, arguing that "[...] A is not inside a factor C, is it?"

Actually, I saw this idiomatic expression here and there, but I need a human confirmation.

  • In French, the closest correct translation would be "A égale B à un facteur C près".
    – keepAlive
    Mar 20 '18 at 15:39
  • 2
    "A is not inside a factor C, is it?" No, but there is some number n within (the range) 0 to C. And n x A = B (or A = n x B). Personally, I'd handle it differently. A differs from B by less than a factor of C (B is reference quantity). A and B differ by less than a factor of C (there isn't a preferred reference quantity).
    – Phil Sweet
    Mar 20 '18 at 17:30

This query can be interpreted more than one way, e.g., as a logical syllogism, as a statistical statement of conditional equality, and perhaps more. Within a factor can be read as 'as a function of C' or, rewriting the whole thing, 'Conditional on C, A equals B' or even 'In the presence of C, A equals B.' In all instances, C is acting as a moderator of the relationship between A and B and in the absence of that moderation, it is implied that A and B have no association and/or are independent.


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