Proving 1-1 Correspondence of I and J Sets

  • Thread starter Zurtex
  • Start date
In summary, 1-1 correspondence is a mathematical concept that describes a one-to-one relationship between two sets, I and J. To prove 1-1 correspondence, you must show that each element in one set has a unique corresponding element in the other set. This is important for easier comparison and analysis of data, and can be proven using various methods. Proving 1-1 correspondence is essentially proving the existence of a bijection between the two sets.
  • #1
Zurtex
Science Advisor
Homework Helper
1,120
1
I have to show that for the sets:

[tex]I = \left\{ x \; | \;0 \leq x \leq 1, x \; \epsilon \; \mathbb{R} \right\}[/tex]
[tex]J = \left\{ x \; | \; 0 \leq x \leq 2, x \; \epsilon \; \mathbb{R} \right\}[/tex]

That I and J are in 1 - 1 correspondence. I don't want to know how to prove this but a hint in the right direction would be really useful if possible.
 
Physics news on Phys.org
  • #2
Apply Schroeder Bernstein Theorem...

-- AI
 
  • #3
TenaliRaman said:
Apply Schroeder Bernstein Theorem...

-- AI
Wow thanks!

Some serious maths rather than the kiddy version of infinite sets we have been learning lol.
 

1. What is the concept of 1-1 correspondence in relation to I and J sets?

1-1 correspondence is a mathematical concept that describes a relationship between two sets, I and J. It means that for every element in set I, there is exactly one corresponding element in set J, and vice versa.

2. How can I prove 1-1 correspondence between I and J sets?

To prove 1-1 correspondence between I and J sets, you must show that every element in set I has a unique corresponding element in set J, and every element in set J has a unique corresponding element in set I. This can be done by creating a mapping between the two sets, where each element in set I is paired with a unique element in set J, and vice versa.

3. What is the importance of proving 1-1 correspondence between I and J sets?

Proving 1-1 correspondence is important because it establishes a one-to-one relationship between two sets, which allows for easier comparison and analysis of data. It also ensures that there are no duplicate or missing elements in either set.

4. Can I use any method to prove 1-1 correspondence between I and J sets?

Yes, there are multiple methods that can be used to prove 1-1 correspondence between I and J sets. Some common methods include creating a mapping between the two sets, using a Venn diagram, or using algebraic equations to show the relationship between the elements in the sets.

5. How does proving 1-1 correspondence relate to the concept of bijection?

Proving 1-1 correspondence is essentially proving that a bijection exists between the two sets, meaning that there is both a one-to-one and an onto relationship between the elements in the sets. This means that every element in set I is paired with a unique element in set J, and vice versa, and there are no elements in either set that do not have a corresponding element in the other set.

Similar threads

2D Fraunhofer-diffraction with infinitely long slits
    • Introductory Physics Homework Help
Replies
9
Views
677
Finding electric potential of an infinite line charge at z axis
    • Introductory Physics Homework Help
2
Replies
64
Views
2K
I Determination of error in interpolating polynomial
    • Calculus
Replies
5
Views
365
On asymptotically stable systems and bounded solutions
    • Calculus and Beyond Homework Help
Replies
4
Views
588
What does a Zener diode do in a circuit with non-ideal voltage source?
    • Introductory Physics Homework Help
Replies
3
Views
227
Calculate the magnetic moment of a rotating sphere
    • Introductory Physics Homework Help
Replies
17
Views
375
Magnetic flux of magnetic field changing as a function of time
    • Introductory Physics Homework Help
Replies
3
Views
1K
Bead sliding along wire with constant horizontal velocity -- Shape of wire?
    • Introductory Physics Homework Help
Replies
2
Views
239
Density of Flow Along a Tube Under the Action of Advancing Piston
    • Introductory Physics Homework Help
Replies
11
Views
671
I Prove that the tail of this distribution goes to zero
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top