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Is the set of positive integers a field under addition and multiplication?
Wiki User
∙ 12y ago
NO. Certainly not. Additive inverse and Multiplicative inverse doesn't exist for many elements.
Wiki User
∙ 12y ago
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What is the field of mathematics?
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics.
What is the difference between arithmetic and math?
Mathematics (math) is a broad field of endeavour, which includes arithmetic. Arithmetic is the part which deals with numbers (and their interactions) only. Other math fields are Number Theory, complex numbers, graph theory, differential calculus, many others.
What is identity property of addiction?
The identity property of addition is a property of a set S with some binary function + (referred to as addition) defined over SxS so that whenever a and b are elements of S, +(a,b) = c is also an element of S. It is common to write +(a,b) as a + b and the definition of such a function creates an algebraic structure over S, usually only as part of some larger structure, ie., a group or a field. The identity property of addition is an axiom that serves to further restrict the type of function + is allowed to be. Specifically, it states that there exists an element of S (for example e), such that for each element a of S, a + e = a. e is usually written as 0, since it behaves like 0 in standard addition over real numbers (0 is the additive identity in the field of real numbers).
What does football have to do with math?
very little besides for keeping score. 6 points for a touchdown 1 point for a field goal as an extra point (after a touchdown) 2 points for either a safety or for passing or running the ball into the endzone as an extra point 3 points for a field goal (not as an extra point) whenever any of the above are achieved, you simply add it to the existing score of the team who achieved it. And that's all that math has to do with football. Simple addition very little besides for keeping score. 6 points for a touchdown 1 point for a field goal as an extra point (after a touchdown) 2 points for either a safety or for passing or running the ball into the endzone as an extra point 3 points for a field goal (not as an extra point) whenever any of the above are achieved, you simply add it to the existing score of the team who achieved it. And that's all that math has to do with football. Simple addition
What's the additive inverse of -7?
We will answers the two questions:1. What is the additive inverse of -72. What's an additive identity.The additive inverse of a number is the number you have to add to the number in order to get 0. (Or more generically speaking, to get the additive identity element of the group or field.) So the additive inverse of -7 is +7. For any real number a, the additive inverse is -a. If z is a complex number, a+bi, then the additive inverse is (-a-bi) since (a+bi)+(-a-bi)=0.The case becomes a little more interesting in fields other than the real or the complex numbers. The integers mod p, where p is a prime, form a finite field. So if we look at integers mod 7, the additive inverse of 5, for example, would be 2 since 5+2=7 which is congruent to 0 in this field.The additive identity in the field of real or complex numbers is 0."Additive identity" means the number you can add to any other number in order to get the same number back. Since -7 + 0 = -7, the additive identity of -7 is 0.In the case of a+bi where i^2=-1, the additive identity is still 0. If it helps you to think of it as 0+0i, that is fine. In the finite field of integers mod p, where p is a prime, we have p as the additive identity. For example, 2 mod 7 is just 2, and if we add 7 it is 9 but that is still 2 mod 7.All of these ideas can be extended to fields of invertible matrices and many other exciting algebraic structures!
Is set of integers is a field?
The set of integers is not closed under multiplication and so is not a field.
Are complex numbers under addition and multiplication a field?
The complex numbers are a field.
Does the set of irrational numbers with the usual addition and multiplication form a field?
Strictly speaking, no, because the identity for addition 0, and the identity for multiplication, 1 are not irrationals.
Which set of numbers forms a field with respect to the operations of addition and multiplication?
whole numbers
Should be distributive property of addition and multiplication have the same answer?
Yes, the Distributive Property is true over addition and multiplication, and it will continue to until you start studying exotic concepts such as Ring Theory or Field Theory.
What are the vector and scalar fields?
In mathematics, a field is a set with certain operators (such as addition and multiplication) defined on it and where the members of the set have certain properties. In a vector field, each member of this set has a value AND a direction associated with it. In a scalar field, there is only vaue but no direction.
The distributive property combines?
Two mathematical operations. In arithmetical structures it is usually multiplication and addition (or subtraction), but in be other pairs of operators defined over a mathematical Field.
What is the distributive property of 588?
588 is a single number. A number does not have a distributive property. The distributive property is exhibited by two binary operations (such as multiplication and addition) defined over a field.
What is the field of mathematics?
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics.
Expressions like 4(3 plus 2) and 4(3) plus 4(2)?
Such expressions illustrate the distributive property of multiplication over addition in the field of real numbers.
How you should know about whole number?
They form a commutative ring in which the primary operation is addition and the secondary operation is multiplication. However, it is not a field because it is not closed under division by a non-zero element.
Properties of real number?
Real numbers have the two basic properties of being an ordered field, and having the least upper bound property. The first says that real numbers comprise a field, with addition and multiplication as well as division by nonzero numbers, which can be totally ordered on a number line in a way compatible with addition and multiplication. The second says that if a nonempty set of real numbers has an upper bound, then it has a least upper bound. These two together define the real numbers completely, and allow its other properties to be deduced.
