0
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.
No.
To say a set is closed under subtraction means that if you subtract any 2 numbers in the set, the answer will always be a member of the set. If you subtract 3 from11, the answer is 8, which is not an odd number. Actually, when you subtract odd numbers, you always get an even number!
Add your answer:
Earn +20 pts
What do interger's allow you to do that whole numbers do not?
Integers are closed under subtraction, meaning that any subtraction problem with integers has a solution in the set of integers.
Is the set of integers that are multiple of 4 is closed under subtraction?
Yes.
Which set is closed under the given operation 1 integers under division 2 negative integers under subtraction 3 odd integers under multiplication?
1 No. 2 No. 3 Yes.
What does this mean Which set of these numbers is closed under subtraction?
It means whatever members of the set you subtract, the answer will still be a member of the set. For example, the set of positive integers is not closed under subtraction, since 3 - 8 = -5
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.
What do interger's allow you to do that whole numbers do not?
Integers are closed under subtraction, meaning that any subtraction problem with integers has a solution in the set of integers.
Is the collection of integers closed under subraction?
Yes, the set of integers is closed under subtraction.
Is the set of integers that are multiple of 4 is closed under subtraction?
Yes.
Is the set of integers closed under subtraction?
yes, because an integer is a positive or negative, rational, whole number. when you subject integers, you still get a positive or negative, rational, whole number, which means that under the closure property of real numbers, the set of integers is closed under subtraction.
Which sets of numbers are closed under subtraction?
To be closed under an operation, when that operation is applied to two member of a set then the result must also be a member of the set. Thus the sets ℂ (Complex numbers), ℝ (Real Numbers), ℚ (Rational Numbers) and ℤ (integers) are closed under subtraction. ℤ+ (the positive integers), ℤ- (the negative integers) and ℕ (the natural numbers) are not closed under subtraction as subtraction can lead to a result which is not a member of the set.
Which set is closed under the given operation 1 integers under division 2 negative integers under subtraction 3 odd integers under multiplication?
1 No. 2 No. 3 Yes.
What does this mean Which set of these numbers is closed under subtraction?
It means whatever members of the set you subtract, the answer will still be a member of the set. For example, the set of positive integers is not closed under subtraction, since 3 - 8 = -5
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.
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.
Why do natural number requires an extension?
Because the set is not closed under subtraction. This led to the set being extended to included negative integers.
What is the difference in subtraction integers and subtracting whole numbers?
None, because the set of integers and the set of whole numbers is the same.
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.
