# Use of "decrease by" in english with a real < 1

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 Lyaudet

• (No native speaker!) The way fractions are read, the denominator works as a number word, so $\frac15$ is "one fifth" not "a one-fifth" to me - I disagree with type 2. I'd use the first variant of the first type, and if you really want to avoid an additive (or rather sutractive) interpretation, say "by 20%" instead of "by $\frac15$". Alternatively, use the second variant of the third type with a neutral verb ("changes by a factor of $\frac45$"); it's okay to use "grow" with a factor $>1$, but "decrease" with a factor $<1$ is at least confusing - one won't say "I lost minus ten dollars" either. Sep 22, 2013 at 10:39

(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.