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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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Related and opposite! english.stackexchange.com/questions/48067 –  Matt Эллен Nov 15 '11 at 10:44
@MattЭллен: Tnx, dimensionless it is. –  SWeko Nov 15 '11 at 10:46
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3 Answers

up vote 10 down vote accepted

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 Nov 15 '11 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 Nov 15 '11 at 12:26
@Urbycoz 1/sec is a dimension. I'm not saying there aren't cases, but frequency is not one of them. –  Matt Эллен Nov 15 '11 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 Nov 15 '11 at 16:34
It's worth noting that "percent", "ppm", "degrees", etc. are not actually synonyms for "dimensionless", but rather are examples of dimensionless units. –  David Z Nov 17 '11 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 Nov 15 '11 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 Nov 15 '11 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 Nov 15 '11 at 12:32
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