Proving Elements of a Set are Distinct

In summary, when asked to prove something about the elements of a set, it is assumed that all the elements are distinct. This is because in order to prove the proposition, all the elements must be distinct. However, it is important to verify with the professor or the question itself if this assumption is correct.
  • #1
JG89
728
1
If a question asks me to prove something about the elements of a set, say {0,1,a,b}, then is it assumed that all elements are distinct?

Because I am attempting a proof, but the only way to prove the proposition is if all elements are distinct. However, it doesn't say in the original question that all elements are distinct, which leads me to my question.
 
Mathematics news on Phys.org
  • #2
JG89 said:
If a question asks me to prove something about the elements of a set, say {0,1,a,b}, then is it assumed that all elements are distinct?

Because I am attempting a proof, but the only way to prove the proposition is if all elements are distinct. However, it doesn't say in the original question that all elements are distinct, which leads me to my question.

Hi JG89! :smile:

Yes, if an exam question defines a set as including particular elements, then they are all distinct. :smile:
 
Last edited:
  • #3
Thanks :)
 
  • #4
tiny-tim said:
Hi JG89! :smile:

Yes, if an exam question defines a set as including particular elements, then they are all distinct. :smile:
Conventions vary. The OP ought to ask his professor before making such a dangerous assumption.
 

FAQ: Proving Elements of a Set are Distinct

How do you prove that elements in a set are distinct?

To prove that elements in a set are distinct, you must show that each element is unique and does not repeat within the set. This can be done by comparing the elements to each other and ensuring that they are all different.

What is the importance of proving elements in a set are distinct?

The importance of proving elements in a set are distinct is to ensure the accuracy and validity of any conclusions drawn from the set. If elements are not distinct, it can lead to incorrect assumptions and faulty reasoning.

What are some common methods for proving distinct elements in a set?

Some common methods for proving distinct elements in a set include using mathematical operations, logical reasoning, and comparing elements directly to each other.

Can elements in a set be both distinct and equal?

No, if elements in a set are distinct, it means they are all unique and different from each other. If elements were also equal, then they would not be distinct.

How can you prove that elements in a set are distinct without comparing them directly?

One way to prove that elements in a set are distinct without comparing them directly is by using the pigeonhole principle. This principle states that if there are more elements in a set than there are distinct values, then at least two elements must share the same value, making them not distinct.

Similar threads

I Subgroup axioms for a symmetric group
Replies
1
Views
944
I Map possible values of a set with a condition to the naturals
Replies
8
Views
1K
I Writing proofs that are more or less formal
Replies
5
Views
2K
MHB Is Every Statement Correct in Defining an Onto Function?
Replies
6
Views
1K
Question about "or" in set theory
Replies
3
Views
2K
I Finding All Automorphisms of Group
Replies
2
Views
2K
MHB Sets and basic notation.
Replies
4
Views
2K
Proving uniqueness of a mathematical object
Replies
12
Views
1K
I Prove that elements of x^i 0<i<n-1 are distinct
Replies
3
Views
1K
Mathematical connection in the cartesian product
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top