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I have heard a number of Cantonese speakers use N (pronounced like the English letter) to designate some sort of unspecified quantity, for instance:

我 N 年前去过。(Approximately "I went there some years ago.")

When did such a usage first come up? Does it have anything to do with the standard mathematical usage of n, and does it also appear in other languages?

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    Math aside, there are lots of examples of mixing "English" into Cantonese in daily use (in Hong Kong). Like 「唔該幫我check下。」「升le (level) 喇,就快升le喇!」「So (show) 料俾人睇」etc. – leo4jc Jul 8 '15 at 18:01
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As you suspected, it is thought to come from the mathematical usage:

为什么“N”可以代表“很多”的意思?例如N多次,N多个

Why can "N" have the meaning "a lot"? For instance, N-times, N-of-them

因为数学上的数列一般都用第N项代表任一项,可知无穷大的一项.

Because in math, sequences usually use "the nth term" to represent any term, including unboundedly large ones.

Another (perhaps more reputable) source

...n在代数中表示很多,如从1开始到2,到3,..., 到n。因此在口语中n经常用来表示特别多,例如“买了n多电话卡”...

...in algebra, "N" signifies "a lot", as in "from 1, 2, 3, up to N". Because of this, in colloquial speech, "N" often is used to express "very many", as in "to buy sooo many telephone cards"...

  • +1, although all the sources you listed are not reliable enough, the language sense tells me that it's true. As a relatively new colloquial usage, I think it may be difficult to dig out the origin. – Stan Jul 10 '15 at 8:05
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As for Cantonese, I had my junior high in Hong Kong during the 80's. I could remember as early as '83 and '84 did we start to say it in school. Etymologically it is 100% mathematical. :) A perfect example of mixing English into the daily Cantonese usage.

The stress is on N when you say it, to emphasis the "countless many"

我打了N次電話都無人接聽!

我睇咗「大時代」N次,次次都咁好睇。

N年前這裡還是一片農地。

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Hm, in Mandarin people will say things like "聽了N次", meaning an unspecified but large number of times. I've heard this since at least the 1980s in Taiwan. I wonder if your example is an extension of the same idiom?

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    Haha, I didn't know it exists in Mandarin as well! – leo4jc Jul 8 '15 at 16:47
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    @leo4jc: I didn't either, though maybe it's more likely that I'll encounter more informal language in Cantonese. – user5714 Jul 8 '15 at 17:44
  • Seen in mainland forums. But I think it's not as common as in HK. Not sure about Taiwan. – velut luna Apr 19 '16 at 12:41

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