Difference between: "both can be viewed as [a task / tasks]…“

Question

What is the difference in comparing plural nouns to a singular noun or a plural noun?

I've seen several versions of comparing noun A to noun B when the noun A is plural. Some sentences use the singular for B others use plural form. For example I recently saw this one:

We will see that these two tasks have a lot in common, and in particular both can be viewed as a task in function approximation.

Source: The Elements of Statistical Learning

As I can see it's perfectly okay to change the above sentence as: "...both can be viewed as tasks..." without changing the meaning of the sentence (at least to me).

So my question is is there any grammar or writing guide for this situation?

Answer 1

It looks unidiomatic to write it like this :

(1) We will see that these two tasks have a lot in common, and in particular both can be viewed as a task in function approximation.

What you have given is good , though not the intended meaning in the Context here [[ thanks to user "Mari-Lou A" for including that ]] :

(2) We will see that these two tasks have a lot in common, and in particular both can be viewed as tasks in function approximation.

Slightly better (though still not the intended meaning) is to drop the "and" & then use "Both" to start a new Sentence :

(3) We will see that these two tasks have a lot in common [:;.] {use Colon or Semicolon or Period here} Both can be viewed as tasks in function approximation.

Even better is this (which is still not the intended meaning) :

(4) We will see that these two tasks have a lot in common, and in particular these two can be viewed as tasks in function approximation.

The meaning is : "task1 is a task in function approximation" & "task2 is a task in function approximation" , in general.

Alternate Context can occur [[ Indeed , that is the Case here ! ]] , where we have to write it like this :

(5) We will see that these two tasks have a lot in common, and in particular these two can be viewed as a single task in function approximation.

The meaning is : "task1 & task2 generally occur together to become a larger task3 which is a single inseparable generalized task in function approximation" , in general.

Example in general : "Identify (x,y) values where y is maximum" is made of 2 tasks : "Identify x" & "Identify y" : Yet , it can be a single inseparable task.

Example in Context : Classification is a technique which converts Input values to Output label , while regression is a technique which converts Input values to Output value. These two tasks can be generalized into a Single task to convert Input numbers into Output function.
[[ Speaking loosely ! This is not a question concerning the technology involved !! ]]