The context is "Every 3 year the total area is increased by a factor of order 3 by adding more stations". I understand that "increase by a factor 10" means increase to 10 times of the original thing, but what is "a factor of order 3"? Thank you very much for your help.

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    It looks like a mistake to me. It should be a factor of 3, an order of 3, or an order of magnitude of 3. For whatever reason, the author confusingly, and mistakenly, combined both factor and order. – Jason Bassford Jan 2 '19 at 8:09
  • Please link to the source – user22427 Jan 2 '19 at 9:01
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    @JasonBassford I agree that the original is a mistake and should almost certainly be just "a factor of 3", but it definitely should not be "an order of magnitude of 3"; "an order of magnitude" is a multiple of 10, sticking the "of 3" on at the end is contradictory and is just as confusing as the original. (You could of course have "3 orders of magnitude" but then you're talking about something 1000 times bigger.) – Hellion Jan 2 '19 at 13:34
  • @hellion Good point. Magnitude of X is mostly redundant. However, it's not wrong to use a number other than 10 in the right context. For instance, a binary numbering system will have numbers increase by a multiples of 2, not 10, and a hexadecimal system would use multiples of 16. So, the multiple of the magnitude used is determined by the numbering system in use—it just happens to most commonly be 10. Of course, it's very unlikely that base 3 is being used in this question. My point was more about the syntax . . . – Jason Bassford Jan 2 '19 at 16:29

Without seeing the phrase in context, I can't say for sure, but my best guess is that the author is using "of order 3" to mean "approximately 3". Or more precisely, I suspect they mean either

  • "closer to 3 than to 1 or 9" (because 9 = 32)
  • "closer to 3 than to 0.3 or 30" (which are 3/10 and 3×10 respectively)

It's impossible to tell based on the information given which of these (if either) was meant, but use of the word "order" implies that the difference between the two of them is not too important anyway.

The phrase "of order [number]", if [number] is a power of 10, is often used to mean "closer to [number] than to any other power of 10". Sometimes people generalize this to use similar phrasing with other numbers like 2, 3, or 5 in which case "of order [number]" can mean "closer to [number] than to any other power of [number]", or it can mean "closer to [number] than to [number/10] or [number ×10]".

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    I think it is probably a mistake too, but sometimes people do say, "on the order of" meaning "approximately" or "roughly". E.g. "Global warming could cause summer temperatures to be something on the order of ten degrees warmer there". So pursuing the possibility this is not a mistake, it could possibly mean "...increased by a factor of roughly 3 ..." However, if that were the intended meaning, it should be, "Every 3 years [pl.] the total area is increased by a factor on the order of 3". As it stands, it would still have two other errors in it anyway. I go with "mistake". – Lorel C. Jan 2 '19 at 22:10
  • @LorelC. To clarify, are you saying that "a factor of order 3" is grammatically incorrect, and it should be "a factor on the order of 3"? That thought hadn't occurred to me. – David Z Jan 2 '19 at 22:27
  • @ David Z I wouldn't call it "grammar" exactly, but "a factor of order 3" doesn't sound right to me. However, I am from the US, and also not well versed in specialized jargon from math, statistics, ... ag(?), or whatever field this selection comes from. – Lorel C. Jan 3 '19 at 0:16
  • @LorelC. Ah, well I'm also from the US, but I have a background in math and physics, and it sounds like perfectly natural phrasing to me. I'm not sure if it's really grammatically correct or not. – David Z Jan 3 '19 at 3:11

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