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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.
What is a rational group?
A rational group is a mathematical concept in group theory that refers to a group whose elements can be expressed in terms of rational numbers or, more generally, in terms of a rational field. Specifically, it often pertains to the study of algebraic groups and their rational points, where the group operations can be defined using rational coefficients. In this context, a group is considered rational if it has a set of generators and relations that can be defined over a rational field, making it possible to analyze its structure within the realm of rational numbers.
Are rational numbers under addition a group?
Yes.
Rational and irrational numbers make up what group?
They make up the Real numbers.
Of integers real numbers rational or irrational numbers what group includes all others?
real
Is the set of rational numbers a commutative group under the operation of division?
No, it is not.
Are most numbers rational or irrational?
The set of irrational numbers is larger than the set of rational numbers, as proved by Cantor: The set of rational numbers is "countable", meaning there is a one-to-one correspondence between the natural numbers and the rational numbers. You can put them in a sequence, in such a way that every rational number will eventually appear in the sequence. The set of irrational numbers is uncountable, this means that no such sequence is possible. All rational and irrationals (ie real numbers) are a subset of complex numbers. Complex numbers, in turn, are part of a larger group, and so on.
Is 3.9 rational or irrational?
If there are no numbers after the 9 it is rational
Do positive rational numbers form group?
Yes, with respect to multiplication but not with respect to addition.
Are some rational numbers are not real numbers?
No. Rational numbers are numbers that can be written as a fraction. All rational numbers are real.
Are rational numbers whole numbers?
The set of rational numbers includes all whole numbers, so SOME rational numbers will also be whole number. But not all rational numbers are whole numbers. So, as a rule, no, rational numbers are not whole numbers.
Why does every rational number have a additive inverse?
The rational numbers form an algebraic structure with respect to addition and this structure is called a group. And it is the property of a group that every element in it has an additive inverse.
