# Should I use “the” or not?

I have a set of values that form a triangle. I want to investigate how the positions of these values affect their denominators. Should I say

1. relationship between the element number and the its denominator
2. relationship between element number and denominator

Should I use "element numbers and denominators". Why?

• I would use 2, because "element number" and "denominator" are mass nouns where you can plug in various items. As such, singular and no article. Or you could think of them as category tags. – user3169 Feb 9 '17 at 0:54

Consider the two sentences below:

Relationship between the element number and its denominator.

and

Relationship between the element number and the denominator.

They both are grammatically correct, however, can mean two different things. You should be able to select the apt sentence based on your mathematical function.

The first sentence uses an 'its' which shows a sense of ownership. From the first sentence, one can deduce that the 'element number' is a numerator. As far as the second sentence is concerned, the element in discussion need not be a numerator.

For example, let us assume that x is a number and y is another, non-zero number.

The first sentence can be mathematically interpreted as the relationship between 'x' and 'y' from the equation:

x / y

However the second sentence can be used to convey the relationship between 'x' and 'y' in an equation like:

x + (z / y)

So, choose wisely, based on your expression.

• Consider "Relationship between EACH element POSITION number and its denominator". 1) "it's" is not the possessive of it. "its" is. 2) The element "number" could be confused with whether it is the first, second, or third and element value. 3) The word "each" enumerates across each pair of value and denominator pair. – Keeta - reinstate Monica Feb 8 '17 at 14:46