Mathmatical proofs help please

  • Thread starter sphelan08
  • Start date
  • Tags
    Proofs
A set is countable if its cardinality is a natural number or 0. A set is uncountable if its cardinality is not a natural number or 0. The union of two sets A and B is the set of all elements that are in A or B.In summary, mathematical proofs involve using definitions of key terms such as uncountable, countable, finite, infinite, and cardinality to prove statements or answer questions. To prove that two uncountable sets have the same cardinality, one could use the fact that a countable union of countable sets is countable. Additionally, the cardinality of a finite set is simply the number of elements in that set, while a set is countable if its
  • #1
sphelan08
1
0
Mathmatical proofs help please!

1. Must two uncountable sets have the same cardinality?
a countable union of countable sets is countable.
Is a finite set necessarily countable?
If the union of A and B is infinite, then A or B must be inifinte



2. Just use definitions of Uncountable, Countable, finite, and infinite, and cardinality to do these proofs.


3. I know what the answers are just by thinking but I cannot prove the answers please help or I will fail
 
Physics news on Phys.org
  • #2


Well, state the definitions, then state what you are thinking and try to use the definitions to prove what you thinking. You have to give us something to go on.
 
  • #3


The cardinality of a finite set is just the number of elements of that set.
 

1. What is a mathematical proof?

A mathematical proof is a rigorous and logical argument that demonstrates the truth or validity of a mathematical statement or theorem. It involves using specific rules and techniques to show that a statement or theorem is true in all cases.

2. Why are mathematical proofs important?

Mathematical proofs are important because they provide a way to verify the accuracy and validity of mathematical statements and theorems. They help to establish a solid foundation for further mathematical discoveries and advancements.

3. How do I write a mathematical proof?

To write a mathematical proof, you must first understand the statement or theorem you are trying to prove. Then, you must use logical reasoning and mathematical techniques to demonstrate the truth of the statement. It is important to clearly state each step and provide evidence for your claims.

4. Are there different types of mathematical proofs?

Yes, there are different types of mathematical proofs, such as direct proofs, indirect proofs, proof by contradiction, and proof by induction. Each type uses different methods and techniques to prove a statement or theorem.

5. How do I know if my mathematical proof is correct?

A good mathematical proof should be clear, concise, and logically sound. It should also provide evidence for each step and clearly explain how the conclusion follows from the given statements. It is important to double check your work and make sure all assumptions and rules are correctly applied.

Similar threads

Prove every subset of countable set is either finite or else countable
    • Calculus and Beyond Homework Help
Replies
1
Views
495
Proof that algebraic numbers are countable
    • Calculus and Beyond Homework Help
Replies
6
Views
2K
Munkres Topology ch1 ex #9 - Generalized DeMorgan's Laws
    • Calculus and Beyond Homework Help
Replies
2
Views
936
In need of proof checking
    • Calculus and Beyond Homework Help
Replies
2
Views
3K
I Is an algorithm for a proof required to halt?
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
Proving that the natural numbers are countable, stuck.
    • Calculus and Beyond Homework Help
Replies
8
Views
2K
I Add an exponential number of elements, what will be the final cardinality?
    • Set Theory, Logic, Probability, Statistics
Replies
16
Views
1K
Union of countable sets is countable
    • Calculus and Beyond Homework Help
Replies
2
Views
2K
Solve Set Theory Question: Can Countably Infinite Set Have Uncountable Subsets?
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
MHB The Set of Borel Sets .... Axler Pages 28-29 .... ....
    • Topology and Analysis
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top