MHB Identity Function: Definition, Examples & Properties

  • Thread starter Thread starter dana1
  • Start date Start date
  • Tags Tags
    Function Identity
Click For Summary
The identity function is defined as a function that maps every element of a set to itself, denoted as $id_A: A \to A$. It is characterized as a bijection, meaning it is both injective and surjective. The composition of the identity function with any other function $f$ results in the original function, expressed as $f \circ id_A = f$. The discussion highlights that the identity function maintains the properties of bijections when composed with other functions. Understanding the identity function is crucial for grasping more complex function properties in mathematics.
dana1
Messages
4
Reaction score
0
hey,
question is attached

thanks in advance!
 

Attachments

  • question2.png
    question2.png
    3.4 KB · Views: 112
Physics news on Phys.org
dana said:
hey,
question is attached

thanks in advance!

Hi dana!

Well... since $id_A: A\to A$ is a bijection, it seems fair to me that $f \circ g: A \to A$ given by $f \circ g: a \mapsto a$ is also a bijection...
 

Thread 'A variant of the Monty Hall problem'

There is a nice little variation of the problem. The host says, after you have chosen the door, that you can change your guess, but to sweeten the deal, he says you can choose the two other doors, if you wish. This proposition is a no brainer, however before you are quick enough to accept it, the host opens one of the two doors and it is empty. In this version you really want to change your pick, but at the same time ask yourself is the host impartial and does that change anything. The host...
View full post »

Similar threads

MHB Can You Help Prove This Combinatorial Identity?
  • · Replies 2 ·
Replies
2
Views
1K
I Choosing from identical objects of different types
  • · Replies 1 ·
Replies
1
Views
2K
Chernoff Bounds using importance sampling identity
  • · Replies 0 ·
Replies
0
Views
2K
A Prove that points which are indistinguishable from 0 exist (using logic)
  • · Replies 17 ·
Replies
17
Views
2K
MHB Properties of the Ordinals ....
  • · Replies 1 ·
Replies
1
Views
1K
MHB Functions and Relations: Proving R is a Function from A to B
  • · Replies 1 ·
Replies
1
Views
1K
I Help understanding conditional expectation identity
  • · Replies 1 ·
Replies
1
Views
2K
MHB Finding MLE for $\theta$ of Statistical Product Model
  • · Replies 6 ·
Replies
6
Views
2K
I Question about about halting problem and this particular function
  • · Replies 54 ·
2
Replies
54
Views
6K
MHB Understanding H&J's Section 3 on Invertible & One-to-One Functions: Q&A
  • · Replies 5 ·
Replies
5
Views
2K