The set of numbers that best describes this situation is given by :
{ -5, -4 , -3, 3, 13}
where we notice we do not repeat the values that appear twice.
Next we need to classify the set of numbers that best describes the following variables:
The number of times "n" a ball bounces
The answer is the set of Natural numbers (1, 2, 3, 4, 5, ...}
which describes the number of bouncings we may see.
The height from which a ball is dropped
In this case, we notice that the whole numbers is not enought, since the height is more of a "continuous" set of possible values with fractional numbers included. so for this set we use the set of positive real numbers.
This in set notation can be written as: x > 0 with x Real number
the hight "x" must be larger than zero so you can drop the ball.
The set to represent years for which computers were sold. We use for this the set of whole numbers (and probably larger than 1981 or so - I don't remember which year the first personal computers were produced} So in set builder notation it will look something like: x >= 1981 or {1981, 1982, 1983, ....} If we are in 2020, the setmay end in 2020:
{ 1981, 1982, 1983, ... ..., 2020} and we would modify the set builder notation to: 1981 <= x <=2020 with x a whole number The important detail is that we are using whole numbers and not real numbers for the years.
The set for the price of the computers, This is nore a set of positive Rational numbers (since you will be having decimals for the cents that go in the price (for example $542.99" and so on. But NOT real numbers because you won't have values associated with irrational numbers like "pi" or square root of 2, etc. Set of rational numbers larger than zero : (x |x > 0 with x rational}