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**Hint:**The particular required set can be compared to the options by actually comparing their constituents. This approach will be easier to be understood. We can compare the given set with all the options one by one and reach an appropriate conclusion. This will provide more clarity to the student.

**Complete step-by-step answer:**

It is stated by the question that we have to find the category to which the set of all negative numbers belong. We know that the set of all negative numbers ranges from zero to negative infinity but excluding zero.

So, negative numbers$ \in \left( { - \infty ,0} \right)$

It refers to all the numbers less than zero.

Now we will compare this set with each of the options one by one.

The natural numbers are actually the positive integers.

$N \in \left\{ {1,2,3, - - - - - - - - - - - - \infty } \right\}$

So, option A) is incorrect.

Integers are numbers positive or negative

$I \in \left\{ { - \infty , - - - - - - , - 2, - 1,0,1, - - - - - - \infty } \right\}$

Option B) is also incorrect.

The positive numbers refer to all the possible numbers that are greater than zero. Its set value ranges from zero to infinity excluding zero.

Positive numbers$ \in \left( {0,\infty } \right)$

So, option C) is also incorrect.

**So, the correct answer is “Option D”.**

**Note:**The student should be able to convert these types of numbers from their definitions into set form.Also students should know classification of number system and their definitions for solving these types of problems.

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