My question is about using "decrease by" without any ambiguity.
I'm reading a paper where the authors consider a set $X$ defined respectively to a tree and an operation on the tree updating the tree and hence an "updated $X$".
They imply the following meaning : $|updated(X)| \leq \frac{4}{5} \cdot |X|$.
But they use three different sentences in two distinct versions of their paper.
Is there a way to remove all ambiguity in the following sentences, what should be considered the correct sentence in english?
First type:
- The size of X decreases by 1/5.
- The size of X decreases by 4/5.
Second type:
- The size of X decreases by a 1/5. (used)
- The size of X decreases by a 4/5.
Third type:
- The size of X decreases by a factor of 1/5. (used)
- The size of X decreases by a factor of 4/5. (used)
The first type seems to me unambiguous but additive. I think it should be interpreted as $|updated(X)| \leq |X| - 1/5$ (ok it doesn't make much sense to remove a real < 1 to a cardinal but the question is valid for any quantity x and is more about natural languages here...).
My feeling is that:
- The size of X decreases by a 1/5.
- The size of X decreases by a factor of 4/5.
are valid if:
- I understand the "a" in the first sentence to denote that 1/5 is a short-hand for "a fifth" (of the global size) that has to be removed (to the global size).
- I understand "decreases by a factor of" as "is multiplied by a factor of (and, by the way, that factor appears to be smaller than one)".
Question 1: What do you consider the correct understanding of these three types of sentences?
Question 2: Can it be unambiguous and "context-free"?
Question 3: Do you know other sentences that are unambiguous and "context-free" to carry this meaning without adding more mathematical notations?
Thanks, best regards,
Laurent Lyaudet1 Answer
$\begingroup$(Native speaker). Completely unambiguous phrases are:
(1) X decreases to 4/5 of its original value
(2) X decreases to 80% of its original value
(3) X decreases by a factor of 1/5
Two fairly unambiguous ones are:
(4) X decreases by 20%
(5) there is a 20% reduction in the value of X
Both of these are ambiguous if X is itself a percentage measure.
Your "second type" is not quite English. A native speaker would say "one fifth" or "a fifth", but would not write "a 1/5".
Also, if it's relevant, there are no differences between various English-speaking countries in this regard, as far as I know.
$\endgroup$
