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Do positive rational numbers form group?
Yes, with respect to multiplication but not with respect to addition.
Is it true that The difference of two rational numbers always a rational number?
Yes. The rational numbers are a closed set with respect to subtraction.
Which set of numbers forms a field with respect to the operations of addition and multiplication?
whole numbers
Are whole numbers closed with respect to multiplication?
Yes. That means that the product of two whole numbers is defined, and that it is again a whole number.
What property links multiplication and addition?
The set of integers is closed with respect to multiplication and with respect to addition.
Do positive rational numbers form group?
Yes, with respect to multiplication but not with respect to addition.
Is it true that The difference of two rational numbers always a rational number?
Yes. The rational numbers are a closed set with respect to subtraction.
Which set of numbers forms a field with respect to the operations of addition and multiplication?
whole numbers
Is the set of all rational numbers continuous?
Continuity is a characteristic of functions not of sets.The set of rational number is infinitely dense. This means that between any two rational numbers, no matter how close together, there are infinitely many rational numbers. And then, between any two of them these is an infinte number of rational numbers, and so on.But, in case that gives you any wrong ideas, between any two rational numbers there is an even higher order of infinity of irrational numbers. In that respect the number of gaps in the set of rational numbers (where the irrational numbers would be) is greater than the cardinality of rational numbers.Continuity is a characteristic of functions not of sets.The set of rational number is infinitely dense. This means that between any two rational numbers, no matter how close together, there are infinitely many rational numbers. And then, between any two of them these is an infinte number of rational numbers, and so on.But, in case that gives you any wrong ideas, between any two rational numbers there is an even higher order of infinity of irrational numbers. In that respect the number of gaps in the set of rational numbers (where the irrational numbers would be) is greater than the cardinality of rational numbers.Continuity is a characteristic of functions not of sets.The set of rational number is infinitely dense. This means that between any two rational numbers, no matter how close together, there are infinitely many rational numbers. And then, between any two of them these is an infinte number of rational numbers, and so on.But, in case that gives you any wrong ideas, between any two rational numbers there is an even higher order of infinity of irrational numbers. In that respect the number of gaps in the set of rational numbers (where the irrational numbers would be) is greater than the cardinality of rational numbers.Continuity is a characteristic of functions not of sets.The set of rational number is infinitely dense. This means that between any two rational numbers, no matter how close together, there are infinitely many rational numbers. And then, between any two of them these is an infinte number of rational numbers, and so on.But, in case that gives you any wrong ideas, between any two rational numbers there is an even higher order of infinity of irrational numbers. In that respect the number of gaps in the set of rational numbers (where the irrational numbers would be) is greater than the cardinality of rational numbers.
Are whole numbers closed with respect to multiplication?
Yes. That means that the product of two whole numbers is defined, and that it is again a whole number.
What property links multiplication and addition?
The set of integers is closed with respect to multiplication and with respect to addition.
What is multiplying a number by 1 that gives a product identical to the given number?
That is because 1 is the identity element of numbers with respect to multiplication.
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.
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.
Is the set -1 closed with respect to multiplication?
No, it is not.
Are the sums and products of whole numbers always whole numbers?
Yes, the whole numbers are closed with respect to addition and multiplication (but not division).The term "whole numbers" is not always consistently defined, but is usually taken to mean either the positive integers or the non-negative integers (the positive integers and zero). In either of these cases, it also isn't closed with respect to subtraction. Some authors treat it as a synonym for "integers", in which case it is closed with respect to subtraction (but still not with respect to division).
Is a set closed with respect to multiplication is it also close with respect to addition?
No. An addition operation need not even be defined.
