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Suppose I have, for example, two sets. Set A has 20 elements and set B has 5 elements. I could say that B is 25 percent the size of A. I'd like a word that would let me succinctly make it clear that a number is a proportion or ratio, but without the need to scale it by 100. So in the previous example, I'd like to say "B is .25 word of A", or something similar.

If I were dealing with probabilities instead of cardinalities, I could say "B will happen with probability/frequency/likelihood x" instead of "B happens x percent of the time". I'd be fine with that sort of form as well.

Right now, I frequently find myself trying to avoid unwieldy sentences like "Converge until the ratio of the number of elements in one of B_i to the number of elements in A is at least x" when I would like to be able to say something analogous to "Converge until at least x percent of A is in one of B_i."

Edit: I may not have been as clear as I'd hoped. It's not that I want to avoid the word percent. Percent is merely the closest word in meaning to the one I'm looking for. Ideally, I want a word such that, given real number x in [0,1], "x (word) of A" is equivalent to "(100 x) percent of A".

x isn't a fixed or known value, so saying things like "1/4 the size" isn't an option. I used specific values in some of the examples in hopes that it would make things clearer, but apparently it had the opposite effect.

"Converge until at least x (word) of A is in one of B_i" is the sort of context in which I would be using it. There certainly exist better ways to phrase it than the alternative I used, but since the goal was to illustrate how unwieldy these alternate phrasings get sometimes, I didn't bother finding a good one for this particular case.

I could use "percent" as long as I replace all instances of "x" with "100x", but since I'm only multiplying by 100 so "percent" can divide by 100 again, that's rather inelegant. I'd like to keep the "The preceding number is a proportion" part of the meaning of percent, but without the "and must be divided by 100 to get the value I'm actually using in all the math" part.

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  • After seeing your edits, surely there are examples of this kind of thing from papers or textbooks in your specific field. Is there some standard language?? – John Feltz Dec 14 '16 at 16:21
  • @JohnFeltz If there is, I haven't noticed it. It's entirely possible that such a word exists and that I have seen it: when text flows well, the word choices don't generally register consciously. And it's not the sort of thing I can search for on Google Scholar. Honestly, I suspect the real answer is "this word doesn't exist". But there's a large enough population of programmers and mathematicians on stackexchange that if the word does exist, someone here will probably know it. – Ray Dec 14 '16 at 22:33
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You don't need a word when you're expressing ratios. Just state the relationship.

B is .25 the size of A

B is one-fourth the size of A

For your more complicated example, fix the awkwardness by moving the comparison and stating the ratio formally.

Converge until the coverage ratio between the elements of B_i and A is 1:4

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  • It looks like there probably isn't a single word that works here. "B is .25 the size of A" is the best of the options suggested, in my opinion. – Ray Dec 22 '16 at 22:30
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Your question is schizophrenic in the sense that first you want to avoid using percent and then you want to embrace it.

I would reword John Feltz's answers slightly.

Your first example: Because you are comparing the sizes of two sets, I would write:

The size of B is 1/4 that of A.

OR

The size of B is 25% that of A.

OR, to be more precise,

The ratio of the size of B to the size of A is 1/4.

There is no need for a word after 1/4 in Options 1 and 3, and in Option 3, it would be incorrect to use 25%.

Your second example: Assuming you want to avoid using percent, I would write:

Converge until the size of at least one of the B_i is 1/4 (or x) that of A.

OR

Converge until the size of at least one of the B_i is 25% (or x%) that of A.

OR, to be more precise,

Converge until the ratio of the size of at least one of the B_i to the size of A is 1/4 (or x).

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You may use the word "times". Though it is typically used when the multiplier is an integer, it can be used in case of a real number multiplier too.

"B is .25 times A"

TFD:

times prep.
Multiplied by: Five times two is ten.

American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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  • B and A are sets. A multiplication operator is not defined on them. – Ray Dec 14 '16 at 22:40
  • @Ray, can you just say b is .25 times a where a and b are cardinalities of A and B respectively? – alwayslearning Dec 16 '16 at 2:52
  • Certainly. There are plenty of other ways to phrase it, as well, but none of them as succinct as I'd like. – Ray Dec 18 '16 at 22:10

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