What is the fewest number of points you must plot in order to have examples of all four sets of​ numbers, including at least one

Answer:

Let’s outline the sets:

Integers: The collection of all whole numbers.

Rational: Numbers that can be expressed as the ratio of two integers.

Natural: The collection of positive integers.

Whole numbers: All the values obtainable by repeatedly adding (or subtracting) 1 to a number.

Thus:

2 qualifies as a:

Whole number, because 1 + 1 = 2 (therefore, it’s also an integer).

We can express 2 as 4/2.

As 2 is the fraction of two integers, it is also considered rational.

Since 2 is positive and an integer, it falls into the category of natural numbers.

Therefore, the number 2 exemplifies all four sets.

If we include a negative example, we can consider -3.

-3 is classified as an integer, is not a whole number, and with 9/-3 = -3, thus it is also a rational number.

Now, addressing the questions:

a) Although a single example can be used across all four sets, I have chosen 2 in this instance.

b) Similarly, I demonstrated that 2, as a positive integer, belongs to all four sets, thus:

Positive integers belong to:

The set of integers.

The set of natural numbers.

The set of rational numbers.

The set of whole numbers.