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What is closed and not-closed under addition?
The set of even numbers is closed under addition, the set of odd numbers is not.
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.
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 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.
What are closed numbers?
It depends on what the number is closed on. For example, even numbers are closed on addition. In other words for any two even numbers that are added, the sum is an even number. Numbers are closed if something applies to all the numbers included within a set. The set above includes only even numbers.
Are even natural numbers closed under division?
Yesss.
What is closed and not-closed under addition?
The set of even numbers is closed under addition, the set of odd numbers is not.
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.
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.
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.
Are even numbers closed under addition?
Yes, when you add any two even numbers, the result is always an even number.
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.
Are even numbers closed under subtraction?
Yes, even numbers are closed under subtraction. When you subtract one even number from another even number, the result is always an even number. This is because both even numbers can be expressed as 2n and 2m (where n and m are integers), and their difference, 2n - 2m, can be factored as 2(n - m), which is also even.
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 are closed numbers?
It depends on what the number is closed on. For example, even numbers are closed on addition. In other words for any two even numbers that are added, the sum is an even number. Numbers are closed if something applies to all the numbers included within a set. The set above includes only even numbers.
Are a set of irrational numbers closed under exponents?
No. Sqrt (2) is irrational. Square it, or raise it to any even power, and it becomes rational. The set is not closed under exponentiation.
