What is closing a rational number under addition And can you close them under subtraction multiplication and division?

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Rational numbers are numbers that can be expressed as a fraction a/b where a and b are both integers and b is not equal to zero. All integers n are rational numbers because they can be expressed as the fraction n/1. Rational numbers are closed under addition, subtraction, multiplication and division by a non-zero rational.
To be closed under addition, subtraction, multiplication and division by a non-zero rational means that if you have two rational numbers, when you add, subtract, multiple or divide them, you will get another rational number.

For example, take the rationals 1/3 and 4/3. When you add them together, you get another rational number, 5/3. Same with the other operations.

1/3 - 4/3 = -1 (remember integers are rational, too)

(1/3) * (4/3) = 4/9

(1/3) / (4/3) = 1/4
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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 (MORE)

Are prime numbers closed under addition?

no, not all prime numbers are closed under addition. why? because, when you add 2 prime numbers you will not always get a prime number. example: 5+3= 8 5 and 3 are prime numbers but their sum is 8 which is a composite number..

Are natural numbers closed under division?

No. Closed means that you could do the operation (division) on any two natural numbers and you would get a result in the natural numbers. Take 7/3 for example, this is obviously not a natural number.

Is the set of irrational numbers closed under subtraction?

No; here's a counterexample to show that the set of irrational numbers is NOT closed under subtraction: pi - pi = 0. pi is an irrational number. If you subtract it from itself, you get zero, which is a rational number. Closure would require that the difference(answer) be an irrational number a (MORE)

Are rational numbers closed under multiplication?

Rational numbers are closed under multiplication, because if you multiply any rational number you will get a pattern. Rational numbers also have a pattern or terminatge, which is good to keep in mind.

Are irrational numbers closed under multiplication?

No. To say a set is closed under multiplication means that if you multiply any two numbers in the set, the result is always a member of the set. If, say, the 2 numbers are radical 2 and radical 2 we have (1.4142...)(1.4142...) which by definition equals 2. The result is not an irrational numbe (MORE)

Is irrational numbers closed under division?

Nope. Quick example: e (2.71828) is irrational. Therefore 2*e is irrational making both of them elements of the set of irrational numbers. However, dividing the two, e/(2*e), gives you 1/2, which is a rational number.

Are odd numbers closed under subtraction?

No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number. No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number. No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number. No, nor unde (MORE)

What is closed under subtraction?

The set of all integers; the set of all rational numbers; the set of all real numbers; the set of all complex numbers. Also their multiples - for example the set of all multiples of 2; the set of all multiples of 2.5; the set of all multiples of sqrt(17); the set of all multiples of (MORE)

Which sets of numbers are closed under subtraction?

To be closed under an operation, when that operation is applied totwo member of a set then the result must also be a member of theset. Thus the sets ℂ (Complex numbers), ℝ (Real Numbers), ℚ (RationalNumbers) and ℤ (integers) are closed under subtraction. ℤ+ (the positive i (MORE)

Are natural numbers closed under addition?

Yes, because naturals are counting numbers, {1,2,3...} and any natural number added by another natural number has to be a natural. Think of a number line, and your adding the natural numbers. The sum has to be natural, so yes it is closed.

Why are fractions closed under addition?

For a set to be closed under any operation, the result of the operation must also be a member of the set. The result of adding fractions is another fraction, thus it is closed under addition. Remember that 8 / 3 , 8 / 4 , 4 / 4 , 2 / 1 are all fractions - they have a numerator and denomin (MORE)

Why is the set of positive whole numbers closed under subtraction?

The set of positive whole numbers is not closed under subtraction! In order for a set of numbers to be closed under some operation would mean that if you take any two elements of that set and use the operation the resulting "answer" would also be in the original set. 26 is a positive whole numb (MORE)

Why are rational numbers closed in subtraction?

Because when one rational number is subtracted from another rational number the result is a rational number. Don't forget that integers (ℤ) are a subset of rational numbers (ℚ).

What is the smallest set of numbers closed under subtraction?

Any one of the sets of the form: {kz : where k is any fixed integer and z belongs to the set of all integers} Thus, k = 1 gives the set of all integers, k = 2 is the set of all even integers, k = 3 is the set of all multiples of 3, and so on. You might think that as k gets larger the sets become (MORE)

Is whole numbers are closed under division?

No, whole numbers are not closed under division. It is possible to divide one whole number by another whole number and get a result which is not a whole number, for example, 1/2. One divided by two is a half.

Is natural numbers a closed set under subtraction?

No. A set is closed under subtraction if when you subtract any two numbers in the set, the answer is always a member of the set. The natural numbers are 1,2,3,4, ... If you subtract 5 from 3 the answer is -2 which is not a natural number.

Are the whole numbers closed under addition if so explain?

Yes because being closed under an operation means that when the operation is performed on members of a set the result is also a member of the set, and when any two [members of the set of] whole numbers are added together the result of the addition is also a whole number which is, unsurprisingly, a m (MORE)

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 (MORE)

Which sets of numbers are closed under multiplication?

There are infinitely many sets of this type. Some of the common sets include natural numbers, integers, rational numbers, real numbers, complex numbers. Also, as an example, all sets of multiples of some whole number, for instance: { ... -6, -4, -2, 0, 2, 4, 6, ...} {... -9, -6, -3, 0, 3, 6, 9, ...} (MORE)