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Why are the rational numbers under the operation of multiplication not a group?
Wiki User
∙ 13y ago
I believe it is because 0 does not have an inverse element.
Wiki User
∙ 13y ago
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Is the set of rational numbers a commutative group under the operation of division?
No, it is not.
Why the set of rationals does not form a group wrt multiplication?
All the elements in a group must be invertible with respect to the operation. The element 0, which belongs to the set does not have an inverse wrt multiplication.
What group of real numbers will 9.34 go to?
A group containing 9.34 is a set of numbers, with some operation defined on the set that also satisfies:closure,associativity,identity, andinvertibility.Two simple groups will be the additive group of 9.34 and all its multiples (including negative ones). The identity is 0.The other is the multiplicative group consisting of all powers of 9.34 and the identity is 1.There can be a finite additive group derived from the first by defining the operation as modulo addition, and similarly with the multiplicative group.Finally, any group that contains one of these groups and also maintains the four conditions listed above, for example, all rational numbers, will also meet the requirements.
Are integers always sometimes or never rational numbers?
All integers are rational numbers, but not all rational numbers are integers.2/1 = 2 is an integer1/2 is not an integerRational numbers are sometimesintegers.
What do rational numbers look like?
Any fraction with integers in the numerator and in the denominator is a rational number.If you write them as decimals, a rational number will either terminate, or the same group of digits will repeat forever, as in 0.33333... or 2.174646464646...
Is the set of irrational numbers a group under the operation of multiplication?
No. It is not even closed. sqrt(3)*sqrt(3) = 3 - which is rational.
Is the set of rational numbers a commutative group under the operation of division?
No, it is not.
Do positive rational numbers form group?
Yes, with respect to multiplication but not with respect to addition.
Why the set of rationals does not form a group wrt multiplication?
All the elements in a group must be invertible with respect to the operation. The element 0, which belongs to the set does not have an inverse wrt multiplication.
Does the set of even integers form a group under the operation of multiplication?
No. The inverses do not belong to the group.
What is a group of rational numbers?
A rational number is a number that can be expressed in fractional form.
Which property would be useful in proving that the product of two rational numbers is always rational?
The fact that the set of rational numbers is a mathematical Group.
Are rational numbers under addition a group?
Yes.
How can closure property help understand the type of solution you might expect with operations?
In a group with closure the solution to the operation must be a number from the same set. The set of integers and the set of rational numbers are closed under addition. So the sum of two (or more) integers must be an integer, the sum of rational numbers must be a rational number.
Is the group of all real numbers except 0 under multiplication is an infinite group?
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Rational and irrational numbers make up what group?
They make up the Real numbers.
What is a group of related multiplication and division facts that use the same numbers?
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