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Does the set of irrational numbers with the usual addition and multiplication form a field?
Wiki User
∙ 14y ago
Strictly speaking, no, because the identity for addition 0, and the identity for multiplication, 1 are not irrationals.
Wiki User
∙ 14y ago
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Which set of numbers forms a field with respect to the operations of addition and multiplication?
whole numbers
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.
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.
Whats the math term for the set of all numbers that are not rational?
It is the set of irrational numbers.* * * * *Though, pedantically, only if the "universal" set is the set of real numbers. A more complete answer could be all numbers in the complex field of the form x + yiwhere y≠0 or y = 0 and x is irrational.
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.
Are complex numbers under addition and multiplication a field?
The complex numbers are a field.
Which set of numbers forms a field with respect to the operations of addition and multiplication?
whole numbers
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.
Is the field irrational numbers complete?
This set cannot be answered since the set of irrational numbers is not a field!
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.
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 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.
Is the set of positive integers a field under addition and multiplication?
NO. Certainly not. Additive inverse and Multiplicative inverse doesn't exist for many elements.
Whats the math term for the set of all numbers that are not rational?
It is the set of irrational numbers.* * * * *Though, pedantically, only if the "universal" set is the set of real numbers. A more complete answer could be all numbers in the complex field of the form x + yiwhere y≠0 or y = 0 and x is irrational.
What are the Similarities between rational and irrational number?
The one thing they have in common is that they are both so-called "real numbers". You can think of them as points on the "real number line".Both are infinitely dense, in the sense that between any two rational numbers, you can find another rational number. The same applies to the irrational numbers. Thus, there are infinitely many of each. However, the infinity of irrational numbers is a larger infinity than that of the rational numbers.
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.
