- #1
Vishera
- 72
- 1
Homework Statement
Homework Equations
The Attempt at a Solution
Why can't C={a1}?
What's wrong with this proof for the set C={a1}?
- Thread starter Vishera
- Start date
-
- Tags
- Proof
Click For Summary
SUMMARY
The discussion centers on the invalidity of the proof concerning the set C={a1}. The key issue arises from the assertion that C={a1} equals B, which leads to the conclusion that an element a2 from set A is not included in either B or C. This contradiction highlights a flaw in the proof, particularly when it states that set A consists of k+1 numbers, which can be either identical or distinct. The proof's failure is established at this juncture, rendering it invalid.
PREREQUISITES- Understanding of set theory concepts, particularly the definitions of sets and elements.
- Familiarity with the principles of mathematical proofs and logical reasoning.
- Knowledge of the notation used in set theory, such as set equality and membership.
- Basic comprehension of the implications of cardinality in sets.
- Study the principles of set theory, focusing on set equality and membership.
- Learn about common pitfalls in mathematical proofs and how to identify them.
- Explore the concept of cardinality and its implications in set theory.
- Review examples of valid and invalid proofs in set theory to enhance understanding.
Students of mathematics, particularly those studying set theory, educators teaching proof techniques, and anyone interested in understanding the nuances of mathematical logic.
Why can't C={a1}?
- #2
AlephZero
Science Advisor
Homework Helper
- 6,999
- 299
Which part of
don't you understand?
- #3
halo31
- 51
- 0
The proof clearly falls apart when it is stated let Set ##A## be a set of ##k+1## numbers. These number can either be all the same, or different. Hence the proof is invalid from that point on.
Similar threads
- · Replies 2 ·
- · Replies 9 ·
- · Replies 5 ·
- · Replies 9 ·
- · Replies 2 ·
- · Replies 24 ·
- · Replies 11 ·
- · Replies 2 ·
- · Replies 7 ·