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I'm translating some documents to English which deal with some measurements. Most of the measurements have a unit dimension (length is in meters, weight is in kilograms, etc) but some of them do not have a specific dimension, e.g. Number of samples.

What word to use to describe such measurements? The direct translation of the original terms leaves me with "undimensional", but I don't think that's it.

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3 Answers 3

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Actually number of samples does have a unit, i.e. samples. So you could say:

I have 101 samples

Just as you can say

I ran 100 km.

So if you are counting something, e.g. samples, apples, people, etc., then use that as the unit.

A quantity without a unit is often a ratio, e.g. a ratio of length (metres) to width (metres) would have no units because metre/metre cancels out; although ratio is probably too broad a term, since it doesn't exclude units.

If you want to represent a number that has no dimension then dimensionless is an accepted term.

Other possible terms:

  • % (percent)
  • ppm (parts per million)
  • degrees

More are listed in the above linked Wikipedia article.

These all depend on what you are measuring.

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  • completely agree, and meter : length :: apple: quantity or count.
    – tenfour
    Commented Nov 15, 2011 at 11:10
  • Strangely, it can in fact be valid to measure things without dimensions. e.g. Frequency can be measured in "per seconds" (slideshare.net/mrrayner/62-describing-waves). But we tend to use "Hertz" instead, because that is an easier concept to grasp.
    – Urbycoz
    Commented Nov 15, 2011 at 12:26
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    @Urbycoz 1/sec is a dimension. I'm not saying there aren't cases, but frequency is not one of them. Commented Nov 15, 2011 at 12:27
  • @Urbycoz - you can also relate any units into length/mass/time (and current). But it's easier to say Volt than kg⋅m^2⋅s^−3⋅A^−1
    – mgb
    Commented Nov 15, 2011 at 16:34
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    It's worth noting that "percent", "ppm", "degrees", etc. are not actually synonyms for "dimensionless", but rather are examples of dimensionless units.
    – David Z
    Commented Nov 17, 2011 at 22:44
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It may depend on the context. However, you could use quantity or amount, even numbers depending on the nature of the object.

It is also a practice to use the hash [#] symbol to represent 'number of'.

I would certainly not use unidimensional unless the focus is actually on that attribute and not the measurement itself.

All the above keeping in mind we are discussing the language part of the issue, not the technicalities.

@Matt: Thanks for the link.

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  • PS: Not raw number, though. That expression is used in various other ways, like unsorted data, unedited data, etc.
    – Kris
    Commented Nov 15, 2011 at 11:00
  • Kris, the focus is exactly on the attribute :) Measurements are grouped by dimension, and I needed a title for the dimensionless group
    – SWeko
    Commented Nov 15, 2011 at 12:34
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Such units for counting are called cardinal numbers.

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    In technical use cardinal numbers implies integer values, and the measurements I have are both integers (number of samples) and real numbers (coefficients)
    – SWeko
    Commented Nov 15, 2011 at 12:32

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