Identity Element: a- = a Property Explained

In summary, an identity element is a special element in a mathematical system that, when combined with any other element, results in the original element. In addition, the identity element in addition is 0 and in multiplication is 1. This concept is important in mathematics as it helps define the structure of a system and is used in various real-world applications like computer programming and physics.
  • #1
Gear300
1,213
9
Is the following property exclusive to the identity elements: a- = a (inverse of a = a)?
 
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  • #2
Nope. For example in Z2, the integers mod 2, you have two elements 0 and 1, and 1+1=0, so 1=-1
 
  • #3
I see. Thanks for the reply.
 

FAQ: Identity Element: a- = a Property Explained

What is an identity element?

An identity element is a special element in a mathematical system that, when combined with any other element in that system, results in the original element. In other words, it leaves the element unchanged.

What is the identity element in addition?

The identity element in addition is 0. When you add 0 to any number, the result is that same number. For example, 0 + 7 = 7.

What is the identity element in multiplication?

The identity element in multiplication is 1. When you multiply any number by 1, the result is that same number. For example, 1 x 5 = 5.

Why is the identity element important in mathematics?

The identity element is important because it helps define the structure of a mathematical system. It is a fundamental property that allows for operations to be performed in a consistent and predictable manner.

How is the identity element used in real-world applications?

The concept of identity element is used in a variety of real-world applications, such as in computer programming, where it is used to define the neutral element in certain operations. It is also used in physics, particularly in the study of vector spaces, where it represents the zero vector or the origin point.

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