Math and Arithmetic

# Is a set of rational numbers a group under subtraction?

###### Wiki User

Yes it has closure, identity, inverse, and an associative property.

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## Related Questions

### Are rational numbers closed under subtraction?

Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.

### Are rational numbers closed under division multiplication addition or subtraction?

Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.

### Is the sum of rational numbers always rational?

Yes. In general, the set of rational numbers is closed under addition, subtraction, and multiplication; and the set of rational numbers without zero is closed under division.

### 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 &#8450; (Complex numbers), &#8477; (Real Numbers), &#8474; (Rational Numbers) and &#8484; (integers) are closed under subtraction. &#8484;+ (the positive integers), &#8484;- (the negative integers) and &#8469; (the natural numbers) are not closed under subtraction as subtraction can lead to a result which is not a member of the set.

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

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

### 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.

### What are irrational numbers closed under?

Irrational numbers are not closed under any of the fundamental operations. You can always find cases where you add two irrational numbers (for example), and get a rational result. On the other hand, the set of real numbers (which includes both rational and irrational numbers) is closed under addition, subtraction, and multiplication - and if you exclude the zero, under division.

### 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 as well, which it isn't. Therefore the set of irrational numbers is NOT closed under subtraction.

### Can the operation subtraction have properties?

Not by itself. A mathematical operation has properties in the context of a set over which it is defined. It is possible to have a set over which properties are not valid.Having said that, the set of rational numbers is closed under subtraction, as is the set of real numbers or complex numbers.Multiplication is distributive over subtraction.

### Which set is closed under the operation of subtraction?

The set of integers, rational numbers, real numbers, complex numbers are some of the sets. Also, many of their subsets: for example, all numbers divisible by 3.

### Are irrational numbers closed under subtraction?

No, they are not. An irrational number subtracted from itself will give 0, which is rational.

### Which set of numbers is closed under subtraction?

A set of real numbers is closed under subtraction when you take two real numbers and subtract , the answer is always a real number .

### 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.

### What are the subsets of real number?

Under real numbers there are rational and irrational numbers.Under rational, there are integers and fractions.Under integers, there are whole numbers, and then under whole numbers, there are natural numbers (counting numbers).I think that's all.

### Why are the set of real numbers is not commuted under subtraction and addition?

Real numbers are commutative (if that is what the question means) under addition. Subtraction is a binary operation defined so that it is not commutative.

### Why are rational numbers not like integers?

The set of rational numbers is closed under division, the set of integers is not.

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