No.
The natural numbers (â„•) are defined in 2 ways:
The set of Integers (ℤ) is the counting numbers, their negatives and zero, ie {..., -3, -2, -1, 0, 1, 2, 3, ...}
No - whole numbers only, no negatives, no fractions
No. Natural numbers may or may not include 0, depending on who you ask (i.e. they can begin 0, 1, 2, 3, … or 1, 2, 3, 4, …), but they don't ever include the negative numbers. However, integers, which are a superset of the natural numbers (i.e. the natural numbers are contained "in" the integers), do include negatives.
The set of integers, of rational numbers, of real numbers, complex numbers and also supersets which contain them.
Whole numbers are usually defined as the number 0,1,2,3,4,5,6.... where "...." means it goes on forever. These are the natural numbers with the number 0 added to them. So the natural numbers are 1,2,3,4,5,6...The integers are all the whole number and all the negatives of the natural numbers....-4,-3,-2,-1,0,1,2,3,4...So every whole number is an integer.Every natural number is an integer.Every integer is NOT a whole number. ( look at -2)Every integer is NOT a natural number. ( look at -3)The set of integers contains the set of natural numbers and contains the set of whole numbers.The set of whole numbers contains the set of natural numbers.
2 negatives make a positive
Natural numbers do not include negatives. Integers do.
Integers.
No - whole numbers only, no negatives, no fractions
9 is a natural number, as is any whole number greater than zero.
No. Natural numbers are a subset of whole numbers. Negative numbers are whole numbers but not natural.
Irrational numbers.
271 of the first 1000 natural numbers contain at least one digit 5. That is 27.1 % of them.
No. Natural numbers may or may not include 0, depending on who you ask (i.e. they can begin 0, 1, 2, 3, … or 1, 2, 3, 4, …), but they don't ever include the negative numbers. However, integers, which are a superset of the natural numbers (i.e. the natural numbers are contained "in" the integers), do include negatives.
The integers are all the natural numbers and their negatives and zero. So 5 is a natural number and negative 5 is its negative. That makes it an integer.
No. 1.68 is not a natural number or a whole number. "Natural" numbers are the counting numbers . . . one, two, three, four . . . 1.68 is not one of them. "Whole" numbers are the integers . . . the natural numbers, their negatives, and zero. 1.68 isn't one of those either. About all you can say for 1.68 is that it's positive, it's mixed, and it's rational.
If N is the set of natural numbers, and the set of whole numbers (integers) is Z, you should be aware that Z also includes negatives and zero, whereas N does not include either of these.
Natural numbers must not contain negative numbers or fractions. Therefore, the square root of 3 = 1.73205080757 is not a natural number