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Show that the set of integers with respect to multiplication is not a group?
Wiki User
∙ 13y ago
To be a group, the set of integers with multiplication has to satisfy certain axioms:
- Associativity: for all integers x,y and z: x(yz) = (xy)z
- Identity element: there exists some integer e such that for all integers x: ex=xe=x
- Inverse elements: for every integer x, there exists an integer y such that xy=yx=e, where e is the identity element
The associativity is satisfied and 1 is clearly the identity element, however no integer other than 1 has an inverse as in the integers xy = 1 implies x=y=1
Wiki User
∙ 13y ago
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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.
Write a multiplication sentence to show the product of any mumber and 1 is?
n x 1 = n
What is the number 2.4 in the form of a fraction using integers to show it's a rational number?
24/10
How Write the number 2.4 in the form using integers to show that it is a rational number.?
2.4 expressed as an improper fraction is 12/5 thus proving that it is a rational number
Write the number 2.4 in the form using integers to show that it is a rational number.?
2.4 is a rational number because it can be expressed as an improper fraction in the form of 12/5
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.
Can you show me a multiplication chart?
show me a multiplication chart
What does estan mean in spanish?
it means to in a way to show respect to another person or a group of boys.
How can you Show that the set of integers is a group with respect to addition?
In abstract algebra, a group is a set with a binary operation that satisfies certain axioms, detailed below. For example, the set of integers with addition is a group. The branch of mathematics which studies groups is called group theory. Many of the structures investigated in mathematics turn out to be groups. These include familiar number systems, such as the integers, the rational numbers, the real numbers, and the complex numbers under addition, as well as the non-zero rationals, reals, and complex numbers, under multiplication. Other important examples are the group of non-singular matrices under multiplication and the group of invertible functions under composition. Group theory allows for the properties of such structures to be investigated in a general setting. Group theory has extensive applications in mathematics, science, and engineering. Many algebraic structures such as fields and vector spaces may be defined concisely in terms of groups, and group theory provides an important tool for studying symmetry, since the symmetries of any object form a group. Groups are thus essential abstractions in branches of physics involving symmetry principles, such as relativity, quantum mechanics, and particle physics. Furthermore, their ability to represent geometric transformations finds applications in chemistry, computer graphics, and other fields.
What is term to show respect for?
Show some respect is the term to use when you want someone to show you respect.
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you can show respect by helping others
How can you show respect for Jehovah's organization?
how to show respect for jehovah;s organization
When was Show Some Respect created?
Show Some Respect was created in 1985.
How will you show respect to your environment?
I can show my appreciation by taking care of it,paticipating in activities that help the environment,showing respect and loving it.
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table of 9
What does a dot in an equation mean?
A dot stands for multiplication. Ways to show multiplication: 10a 10 x a 10(a) 10 *dot* a
How do the Japanese people show respect?
There are many different ways that the Japanese show respect. Their entire culture is based on respect.
