# Thread: Why is this true ?

1. ## Why is this true ?

In ordered structures, the book says that

A^1 != A

In the example, they say :

Let A = {a,b,c}

A^1 = { (a) , (b), (c) }

How does the parentheses make them different ?

2. Originally Posted by Matter_Math
In ordered structures, the book says that

A^1 != A

In the example, they say :

Let A = {a,b,c}

A^1 = { (a) , (b), (c) }

How does the parentheses make them different ?
Firstly, saying $A^1 != A$ is not a good practice on a math website. We don't do C++ here, it's $A^1\ne A$. And, although I have actually not seen this notation before my gut tells me that it means $A^1=\left\{\{a\}:a\in A\right\}$ which clearly, set theoretically that is, is not equal to $A$.

3. Originally Posted by Drexel28
Firstly, saying $A^1 != A$ is not a good practice on a math website. We don't do C++ here, it's $A^1\ne A$. And, although I have actually not seen this notation before my gut tells me that it means $A^1=\left\{\{a\}:a\in A\right\}$ which clearly, set theoretically that is, is not equal to $A$.

Oh thanks. I am new to formating words, sorry.

$A^1=\left\{\{a\}:a\in A\right\}$

This is the same in my book. Does that read, A^1 equals the all the
pair (a) in which a is a element in A ?

Sorry I am new to this completely.

4. Originally Posted by Matter_Math
Oh thanks. I am new to formating words, sorry.

$A^1=\left\{\{a\}:a\in A\right\}$

This is the same in my book. Does that read, A^1 equals the all the
pair (a) in which a is a element in A ?

Sorry I am new to this completely.
It's no problem. I have no idea what your book means. I would interpret it like this. $A^1$ is the set of all singletons in $\wp\left(A\right)$. In other words, take each element of $A$ put it in it's own set and then put it back. And as sets we have that $a\ne\{a\}$.

5. Originally Posted by Matter_Math
This is the same in my book. Does that read, A^1 equals the all the pair (a) in which a is a element in A ?
Who is the author to your text book and what is the course name?

6. Originally Posted by Plato
Who is the author to your text book and what is the course name?

The above was not stated in the book, it was by bad interpretation, sorry.

My book is called : Discrete Structures, Logic , and Computability
by James L. Hein, 3rd edition.

and the course name is called Discrete Systems.