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Which set of numbers forms a field with respect to the operations of addition and multiplication?
Wiki User
∙ 10y ago
whole numbers
Wiki User
∙ 10y ago
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Do positive rational numbers form group?
Yes, with respect to multiplication but not with respect to addition.
What property links multiplication and addition?
The set of integers is closed with respect to multiplication and with respect to addition.
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.
Which of the basic rules of arithmetic are true when you restrict the number system to the positive integers?
Closure with respect to addition and multiplication. Cummutative, Associative properties of addition and of multiplication. Distributive property of multiplication over addition.
Are rational numbers are commutative with respect to multiplication?
Yes, they are.
Do positive rational numbers form group?
Yes, with respect to multiplication but not with respect to addition.
What property links multiplication and addition?
The set of integers is closed with respect to multiplication and with respect to addition.
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.
Which of the basic rules of arithmetic are true when you restrict the number system to the positive integers?
Closure with respect to addition and multiplication. Cummutative, Associative properties of addition and of multiplication. Distributive property of multiplication over addition.
Are rational numbers are commutative with respect to multiplication?
Yes, they are.
Why do the natural numbers need an extension?
While natural numbers are closed with respect to addition and mulitplication, they are missing the additive identity (zero). Furthermore, they are not closed with respect to two of the fundamental operations of arithmetic: subtraction and division.
What are the fundamental operations of integers?
I am not sure there are any fundamental operations of integers. The fundamental operations of arithmetic are addition, subtraction, multiplication and division. However, the set of integers is not closed with respect to division: that is, the division of one integer by another does not necessarily result in an integer.
What is the mathematical term commute?
Change the order of the terms. If A + B = B + A then A and B are said to commute with respect to addition. Although this may seem trivially true in the case of numbers and addition as "normally" defined, it is not true with respect to many mathematical operations.
The set of whole numbers and there opposites?
The question cannot be answered sensibly for two main reasons.First, the question mentions "there opposites" but does not specify WHERE the "there" refers to. Second, opposites are defined in the context of some operation. The opposite of 3 with respect to addition is -3 while the opposite with respect to multiplication is 1/3. There are other operations which will give yet more "opposites". There is no way of determining which one you mean.
Is 1 the identity element or a whole number?
1 is a whole number. It is the identity element with respect to multiplication but not addition.
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).
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.
