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Is there a subset of the natural numbers that is closed for addition?
Yes. The entire set of natural numbers is closed under addition (but not subtraction). So are the even numbers (but not the odd numbers), the multiples of 3, of 4, etc.
What is a set of rational numbers not closed under?
It is not closed under taking square (or other even) roots.
Are even natural numbers closed under division?
Yesss.
Is the set of integers is close under subtraction?
Yes, because suppose that 'a' and 'b' are both arbitrary integers. Then (a-b) or (b-a) will then provide you with another integer. Suppose that the integer you are given from (a-b) is not unique. Then we have: (a-b)=c and (a-b)=c' Then, trivially, since (a-b)=(a-b), we have c=c'. Thus it is closed under subtraction.
Why are even whole and natural numbers closed under addition?
For a set to be closed under an operation, doing the operations on any two members of the set must result in another member of the set.The set of even natural numbers is {2, 4, 6, ...}.When two even numbers are added, the result is also an even number.Adding two positive numbers results in a larger positive number.Thus, adding two even natural numbers together results in another even natural number and so is closed.The set of even whole numbers is {..., -6, -4, -2, 0, 2, 4, 6, ...}.When two even numbers are added, the result is also an even number.It does not matter which combination of positive and negative whole numbers are added as all positive and negative whole numbers (including zero) are in the set. Thus it is also closed under addition.
Is there a subset of the natural numbers that is closed for addition?
Yes. The entire set of natural numbers is closed under addition (but not subtraction). So are the even numbers (but not the odd numbers), the multiples of 3, of 4, etc.
What is closed and not-closed under addition?
The set of even numbers is closed under addition, the set of odd numbers is not.
Is the set of even integers closed under subtraction and division?
Subtraction: Yes. Division: No. 2/4 = is not an integer, let alone an even integer.
Why are odd integers closed under multiplication but not under addition?
The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
What is a set of rational numbers not closed under?
It is not closed under taking square (or other even) roots.
Are even natural numbers closed under division?
Yesss.
Is the set of even whole numbers closed under multiplication?
Yes, it is closed. This means that if you multiply two even number, you again get a number within the set of even numbers.
Are even numbers closed under addition?
Yes, when you add any two even numbers, the result is always an even number.
Is the set of integers is close under subtraction?
Yes, because suppose that 'a' and 'b' are both arbitrary integers. Then (a-b) or (b-a) will then provide you with another integer. Suppose that the integer you are given from (a-b) is not unique. Then we have: (a-b)=c and (a-b)=c' Then, trivially, since (a-b)=(a-b), we have c=c'. Thus it is closed under subtraction.
The set of even numbers is closed under division?
No. 2/4 is not an even number.
Is subtraction of even whole numbers closed?
Unfortunately, the term "whole numbers" is somewhat ambiguous - it means different things to different people. If you mean "integers", yes, it is closed. If you mean "positive integers" or "non-negative integers", no, it isn't.
Are even numbers closed for addition?
Yes, the sum of any two even numbers is an even number. This means they are closed under addition. Closure Property: For every even number a, for every even number b, a + b is an even number.
