When people say things like "we have a wide variety of products" or "product x can run in a variety of modes", what is the lowest number of modes or products which one can comfortably call a variety? Is having 2 things, a red and blue widget say, a satisfactory quantity to call "a variety of widgets" ? If not a simple number, perhaps it would be the level of differences between the things? I could safely declare a variety of widgets (red and blue) but not a variety of products (I just have widgets). Thoughts?

Apologies if this is not really "mathematics" but you folk seem to be the perfect group and this sort of comes down to sets perhaps.


closed as off-topic by Arthur, lioness99a, Namaste, pwerth, Eric Wofsey Jan 25 at 21:42

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  • "This question is not about mathematics, within the scope defined in the help center." – Arthur, lioness99a, Namaste, pwerth, Eric Wofsey
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  • $\begingroup$ It's a language thing (and a marketing thing), not a mathematics thing. Marketers are (depending on country) allowed to say basically whatever they want. Especially when using vague words like "variety" and "many". So without reading minds, there is no way to know what they mean when they say it. Nor is it possible to tell whether they mean what they say. $\endgroup$ – Arthur Jan 25 at 12:25
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    $\begingroup$ This is maybe a question for "English Language and Usage". $\endgroup$ – Mark S. Jan 25 at 13:19
  • $\begingroup$ @Arthur - I am sure they don't mean what they say....marketeers that is :) $\endgroup$ – Jon Holland Jan 25 at 13:26
  • $\begingroup$ This is clearly related to the Sorites paradox. $\endgroup$ – Somos Jan 25 at 14:47
  • $\begingroup$ @Somos Ah yes I have also been considering (another marketing term) the use of "heaps of..." in descriptions and wondering what one could call a heap ... and when it doesn't conform to that description. The Sorites paradox is very interesting - thanks $\endgroup$ – Jon Holland Jan 28 at 9:34

As mentioned in the comments, this is really an issue of language and psychology. For example, linguists have studied the different concepts and vocabulary that are used in different languages.

The mathematical approach would be to recognise that "wide variety" isn't well defined and either avoid it or say something like "For the purposes of this problem, I will treat a wide variety of $x$ as meaning . . . " and proceed to define it in whatever way suits the problem at hand.

  • $\begingroup$ Yes fair enough. It is down to semantics really - but I wondered if there was a mathematical definition. $\endgroup$ – Jon Holland Jan 25 at 13:27
  • $\begingroup$ @JonHolland I think it can be understood variius ways (linguistic asoect) but that many of those might be translatable into mathematical definitions. I might add a few if I think of them and have the energy. $\endgroup$ – timtfj Jan 25 at 14:31
  • $\begingroup$ @JonHolland For example we could perhaps decide "they had a wide variety of incomes" means "the standard deviation in their incomes was at least double what it is for the general population". $\endgroup$ – timtfj Jan 25 at 14:37
  • $\begingroup$ yes that is an interesting line of thought $\endgroup$ – Jon Holland Jan 28 at 9:32
  • $\begingroup$ @JonHolland When people use a phrase they do usually mean something, and it can be interesting finding a way to express ir. :-) $\endgroup$ – timtfj Jan 28 at 11:35

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