0
What else can I help you with?
Is the set of odd whole numbers for division open or closed?
The set of odd whole numbers is neither open nor closed in the context of standard topology on the real numbers. In topology, a set is considered closed if it contains all its limit points; however, odd whole numbers do not include any even numbers or fractions, which means they do not contain limit points that approach them. Additionally, they are not an open set because there are no neighborhoods around any of the odd whole numbers that entirely consist of odd whole numbers.
Why do whole numbers need an extension?
The first need arose when it was found that the set of whole numbers was not closed under division. That is, given whole numbers A and B (B non-zero), that, in general, A/B was not a whole number - but a fraction.
Are the set of rational numbers closed under division?
No, it is not. Division by zero (a rational) is not defined.
What is the set of whole numbers closed by?
If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.
Is Division closed in Real?
No, since you can't divide by zero. On the other hand, the set of real numbers without zero is closed under division.
Why do whole number require an extension?
The set of whole numbers is not closed under division (by non-zero whole numbers).
What set of numbers is closed under division?
Integers are closed under division I think o.o. It's either counting numbers, integers or whole numbers . I cant remember :/
Is the set of odd whole numbers for division open or closed?
The set of odd whole numbers is neither open nor closed in the context of standard topology on the real numbers. In topology, a set is considered closed if it contains all its limit points; however, odd whole numbers do not include any even numbers or fractions, which means they do not contain limit points that approach them. Additionally, they are not an open set because there are no neighborhoods around any of the odd whole numbers that entirely consist of odd whole numbers.
What is the principle of closure math?
When you combine any two numbers in a set the result is also in that set. e.g. The set of whole numbers is closed with respect to addition, subtraction and multiplication. i.e. when you add, subtract or multiply two numbers the answer will always be a whole number. But the set of whole numbers is NOT closed with respect to division as the answer is not always a whole number e.g. 7÷5=1.4 The answer is not a whole number.
Why do you think that rational numbers are important?
The set of whole numbers is not closed under division by a non-zero whole number. Rational numbers provide that closure and so enable the definition of division of one integer by a non-zero integer.
Is the set of whole numbers closed under subtraction?
It depends on your definition of whole numbers. The classic definition of whole numbers is the set of counting numbers and zero. In this case, the set of whole numbers is not closed under subtraction, because 3-6 = -3, and -3 is not a member of this set. However, if you use whole numbers as the set of all integers, then whole numbers would be closed under subtraction.
Why do whole numbers need an extension?
The first need arose when it was found that the set of whole numbers was not closed under division. That is, given whole numbers A and B (B non-zero), that, in general, A/B was not a whole number - but a fraction.
What does this mean Which set of these numbers is closed under division?
It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.
Is the set of real numbers closed under addition?
Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.
Are the set of rational numbers closed under division?
No, it is not. Division by zero (a rational) is not defined.
Why are rational numbers not like integers?
The set of rational numbers is closed under division, the set of integers is not.
Is the set of whole numbers are closed under multiplication?
If you can never, by multiplying two whole numbers, get anything but another whole number back as your answer, then, YES, the set of whole numbers must be closed under multiplication.
