How can I prove it? (injection, bijection, surjection)

Click For Summary

Homework Help Overview

The discussion revolves around proving properties of functions, specifically focusing on the implications of a composition of functions being bijective. The subject area includes concepts of injective, surjective, and bijective functions in mathematics.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants are questioning the meanings of terms such as "g°f," "bijective," "surjective," and "injective." Some suggest starting with definitions to explore the relationships between these concepts. Others express difficulty in articulating their thoughts mathematically despite visualizing the concepts.

Discussion Status

The discussion is ongoing, with participants exploring definitions and implications of the terms involved. There is an acknowledgment of the need to clarify foundational concepts before proceeding with the proof.

Contextual Notes

Participants have noted challenges in expressing their reasoning mathematically, which may affect the progression of the discussion. There is an emphasis on understanding definitions as a precursor to proving the statement.

gotmejerry
Messages
9
Reaction score
0

Homework Statement


How can I prove this?

If g°f is a bijective function, then g is surjective and f is injective.

Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
First what does g°f mean
what does bijective mean
what does surjective mean
what does injective mean
 
Start of with let g of f be a bijection, than state of the definition of a bijection. From there you can prove what must be true of g and f for g of f to meet the definition.
 
I can see why it is need to be true, when I draw it, unfotunately I cannot write down the solution in a mathematical way.
 
To start say
Let g°f be a bijective function.

then what can you say about g°f
 

Similar threads

F bijective <=> f has an inverse
  • · Replies 7 ·
Replies
7
Views
3K
Prove that an endomorphism is injective iff it is surjective
  • · Replies 1 ·
Replies
1
Views
2K
Show injectivity, surjectivity and kernel of groups
  • · Replies 1 ·
Replies
1
Views
2K
Finding the range of a function when checking if it is bijective
  • · Replies 12 ·
Replies
12
Views
2K
Given surjective ##T:V\to W##, find isomorphism ##T|_U## of U onto W.
  • · Replies 1 ·
Replies
1
Views
2K
Euclidean Group Maps: Proving Injectivity, Surjectivity, and Inverses
  • · Replies 3 ·
Replies
3
Views
2K
Prove that every subset ##B## of ##A=\{1,...,n\}## is finite
  • · Replies 4 ·
Replies
4
Views
1K
Prove every subset of countable set is either finite or else countable
  • · Replies 1 ·
Replies
1
Views
2K
Prove that this mapping is a bijection
  • · Replies 9 ·
Replies
9
Views
2K
Injective & Surjective Functions
  • · Replies 9 ·
Replies
9
Views
3K