Last Updated on September 10, 2026 by Maged kamel
The difference between the counting numbers and the whole numbers.
This is the second lecture about sets. We will start by introducing solved prob ems. The counting numbers must be written as a set. The counting numbers are 1, 2, 3, 4, and so on. If we need whole numbers, as we discussed earlier, include zero in the set. The set form is shown.
What are Integers?
We will proceed to discuss whole numbers. If we want to include the minus sign, we need integers.
The integers are like whole numbers, but they also include negative numbers.
The whole numbers start at 0 and go to infinity. Now, still no fractions or decimals; include the (+) and (-) signs, but do not include fractions or decimals. Iquo:e so that integers can be negative (-1, -2, -3, ….). They extend to infinity and include positive integers (1, 2, 3,…). Zero is bolded and considered a standalone element.
Types of Integers.
The following slide will demonstrate that when dealing with negative numbers, we move to the left, indicating -1, -2, -3, -4, and -5. With positive numbers, we move to the right, writing +1, +2, +3, +4, and +5. Zero is also included with all the positive numbers.
Remember that for the negative numbers, 0 was not there. So, what numbers are missing? These numbers are + and 0, so when saying nonnegative it includes 0 and positive numbers. Suppose we need to include non-positive integers.
Zero should be there, as should all the negative numbers. 0 is a standalone element and is included, while non-negatives or non-positives are excluded.
Solved problems 1 and 2.
We will check another solved problem: Which one of the following is not a whole number? Four answers were given: +5, +10, -3, +8. The correct answer is C: -3 is a negative number and thus not a whole number. C is the correct answer because it is not a whole number, as it is negative.
For problem 2, which of the following is not an integer? 10, 2, 8, 1/4. The integers include zero and positive and negative numbers; non-integers are fractions or decimals. Option D is not an integer, A is a negative integer, and B and C are positive integers. D is selected.
Solved problem-3.
For solved problem 3, which of the following describes the given set? {…, -5, -4, -3, -2, -1, 0}. The dots show that we have negative numbers approaching negative infinity; reading them, we have 0, -1, -2, -3, -4, -5.
We need an Expression that describes the set’s contents. This justification for the set builder has four options; we need to select the correct one. The first choice states that the set consists of negative whole numbers.
The second choice states that the set is Non-(+ve) numbers. The third choice states that the set is of negative numbers. The fourth choice states that the set is nonnegative numbers. For the first choice, the set is negative whole numbers. There are no negative whole numbers.
The entire set of numbers is (0, 1, 2, 3, 4, 5…) For the second choice, the set is the set of non-positive numbers. For non-positive integers, this choice is correct, since they include 0 and negative numbers. For the third choice, the set is a set of negative integers.
What are the negative integers? The negative integers include all negative numbers, but they do not include zero, which is not true of the given set.
This statement holds if the given set excludes zero. For the fourth choice, the set is of nonnegative numbers. This statement is wrong, since the set includes zero and all negative numbers. The correct answer is b: the set of non-positive numbers.
Solved example -4.
For solved problem number 4, he draws a line from 0 to. A d also draw -1, -2, -3, -4, -5 Q letter is placed at -4, the letter A is at -2.50, letter B at -1, and letter B’ t 0. Letter F is at +1, letter C at +2.5, and letter D at +4.
From the figure, how many positive numbers are there compared to negative numbers? The positive numbers should be greater than the negative numbers, but by how much?
The four options were given. Let us check together so you can participate in the answer and see why we chose C as the correct answer: 1. For positive numbers, there is no decimal or fraction, whether positive or negative so that we will exclude the fraction items since the value = -2.50.
We will exclude c since it is 2.5. How many positive letters? We have F, d,e. A ain, how many negative letters do you have with no fraction or decimal? We have B, Q.
So 3-2=1, then c is the correct ch ice. Check the analysis now. A is not a number since it is a frfractionc is not an integer, we have -2.50 B’ is ero. N is positive, negative, or nonnegative. The positive figures are F, D, and E. Negative figures are B and Q.
Solved problem -5.
Example 5: Which of the following is correctly described set of whole numbers is written as {…, -4, -3,-2, -1, 0}. The first option is the set of whole numbers less than 4.
The second option is the set of whole numbers = 4. The third option is the set of integers less than or equal to 4.
If we said that a set is a whole number, this is not true, since the set of whole numbers includes all positive integers.
The first two options are not valid; we’re left with I,
We have two options: the set of Integers <= +4 or >= -4 and = 4? Let us check option no. 4.
If we choose this option, we will select the positive and negative Integers.
If we select option 4,>= -4 and <= 4, it gives us a set of this form, extending from -4 to 4. Since it is an Integer, it contains both positive and negative numbers. However, our given set extends to negative infinity.
Selecting option 4 will not yield the correct set, as our last term will be. The proper solution is option 3. For review, we first checked that the given set is not a set of whole numbers. Then we selected the right option between 3 and 4.
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