Last Updated on March 21, 2024 by Maged kamel

The difference between the Counting number and the Whole number.

This is the second lecture about sets. We will start by introducing solved problems. It is required to write the counting numbers in a form of a set. The counting number is 1,2,3,4, then dots. If it is required to make the whole number as we have discussed earlier, Then the zero should be included in the set braces. The set form is shown.

What are Integers?

We will proceed to talk about the Integers. If we want to include the minus sign, then we need to have the Integers.
The Integers are like whole numbers, but they also include negative numbers.

The whole number starts from 0 to infinity. Now for Integers, still no fraction, no decimal, include the (+) and (-) signs but do not include fractions or decimals. I quote, so Integers can be negative (-1, -2, -3,-4,-5,…) and extend to infinity. and include positive (+1, +2, +3,+4,+5,…) extend to infinity. The zero 0 is made bold and considered a stand-alone element.

Types of integers.

The next slide will show that While dealing with the negative numbers, we are moving towards the left, we are saying -1,-2,-3,-4,-5, dots. While dealing with the positive numbers, we are moving towards the right, we are saying +1,+2,+3,+4,+5, dots. The zero will be present also all the positive numbers.

Remember that for the negative numbers, 0 was not there. So what are the numbers that are not there? these numbers are + and 0, so when saying nonnegative.
We have to include 0 and +ve numbers. Suppose we need to include the non-positive integers. The zero should be there and all the negative numbers. 0 is a standalone element and is included while excluding Non- negative Integers or nonpositive integers.

Solved problems 1&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, so it is not a whole number. C is the correct answer for not whole numbers because it is negative.

For solved problem 2, which one of the following is not an Integer? 10, 2, 8,1/4. The integer includes zero, +ve, and negative numbers, for non Integer, it should be a fraction or decimal. Option d is not an Integer, A is a negative Integer and band c is a positive integer. 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 explain that we have negative numbers till infinity, if we read, we have 0,-1,-2,-3,-4,-5. We need the expression that describes the content of the set. This is justification for the set builder Four options are given, we need to select one of these choices, which is the correct one. The first choice, the set is a negative whole number.
The second choice, the set is Non -(+ve) Integers. The third choice, the set is of -ve integers. The fourth choice, the set is Non-( -ve) Integers. For the first choice, a set is a negative whole number.  We know that there are no negative whole numbers. The whole number is ( 0, 1, 2,3, 4, 5,…).  For the second choice, the set is non-positive integers. Non-positive Integers, this choice is correct. since non-positive integers include 0 and -ve numbers. For the third choice, the set is of negative Integers.

   What are the negative Integers? the negative Integers include all the negative values of numbers to infinity, but this does not include zero, which is not the case of the given set.
   This statement could hold good if the given set excludes zero. For the fourth choice, the set is of non-negative Integers. The statement is wrong since the given set includes zero and all negative numbers. Then the correct answer is b, which is the set is non-( +ve) Integers.

Solved example -4.

For solved problem number 4, he draws like a roller 0, 1,2,3,4,5. and 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’ at 0. Letter F is at +1, letter C at +2.5, and letter d at +4. Letter e is at +5. From the figure, how many of the positive Integers are more than the negative integers? The positive numbers should be more than the negative … numbers, but the question is how many more?

The four options were given. let us check together so that you participate in the answer. and check why we have chosen c as the correct answer. which is 1. For +ve Integers, there is no decimal or fraction, whether +ve or negative, so 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. Again how many negative letters with no fraction or decimal? we have B, Q.so 3-2=1, then c is the correct choice. check the analysis now, A is not an integer since it is a fraction. c is not Integers, we have -2.50 B’ is zero. not Positive negative, or nonnegative. The positive figures are F,d,e. The negative figures are B and Q.

Solved problem -5.

Example 5, Which of the following is correctly described? The set of the whole number is written as {…, -4, -3,-2, -1,0 }. The first option is the set of the whole number of less than 4.

The second option is the set of the whole number of The <= 4. The third option is the set of the Integers which is <= 4.

If we said that a set is a whole number, this is not true, since the whole number includes all positive numbers.
The first two options are not valid. We are left with I,
We have two options to select one of them, whether the set of Integers <=+4 or>=-4 and <=4? Let us check option number no.4, if we choose this option, we will select the positive and negative Integers.

If we select option 4 for >=-4 and Less<=4, it will give us a set of this form extending from 4 to -4, since it is an Integer it contains both+ve and -ve. But our given set is continuous to infinity in the minus numbers.

Selecting option 4 will not give us the right set as given since our last term will be -4. The correct solution will be option 3. For a review, we checked first that the given set is not a whole number. Then select the right option between 3 and 4.

For a useful external site, math is fun, and valuable data about whole numbers and integers.
For the next post, Definition of absolute value, rational numbers, and fractions.