Set Problems: Is My Statement about Circles True?

  • Context: MHB 
  • Thread starter Thread starter jaychay
  • Start date Start date
  • Tags Tags
    Set
Click For Summary
SUMMARY

The discussion centers on the properties of the empty set, denoted as $\emptyset$, and its relationship to other sets. It is established that while the empty set is a subset of every set, it is not an element of any set that contains specific elements. For example, $\emptyset$ is a subset of the set $\{1, 2, 3\}$, but it is not an element of that set. This distinction clarifies common misconceptions regarding set theory.

PREREQUISITES
  • Understanding of set theory concepts
  • Familiarity with the notation of subsets and elements
  • Knowledge of the properties of the empty set
  • Basic mathematical logic
NEXT STEPS
  • Research the properties of subsets in set theory
  • Study the implications of the empty set in mathematical proofs
  • Learn about different types of sets, including finite and infinite sets
  • Explore advanced topics in set theory, such as power sets and Cartesian products
USEFUL FOR

Students of mathematics, educators teaching set theory, and anyone interested in the foundational concepts of mathematical logic and set relationships.

jaychay
Messages
58
Reaction score
0
Untitled v.png


Is the statement that I have circle is true ?
Because I feel like the solution in my textbook is wrong, I only learn that empty set is a subset of every set but it is not an element of a set.
 
Physics news on Phys.org
You are right: $\emptyset$ is not an element of $\{1, 2, 3\}$. The only elements of that set are 1, 2 and 3.
 
Of course, the empty set, $\phi$, is a subset of every set so it is true that $\phi\subset \{1, 2, 3\}$.
 

Similar threads

Undergrad Relation of the empty set to vacuous truth?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Why is the empty set a proper subset of every set?
  • · Replies 13 ·
Replies
13
Views
13K
MHB Is Every Statement Correct in Defining an Onto Function?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad (0,1) is uncountable using binary expansions?
  • · Replies 15 ·
Replies
15
Views
3K
MHB Sets and basic notation.
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Question about "or" in set theory
  • · Replies 3 ·
Replies
3
Views
2K
High School Is everything in math either an axiom or a theorem?
  • · Replies 72 ·
3
Replies
72
Views
8K
Graduate Can you use Taylor Series with mathematical objects other than points?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate How would you define a mathematical space?
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Calculating the odds of drawing 3 "no" notes from a hat with 3 "no" and 3 "yes" notes
  • · Replies 3 ·
Replies
3
Views
2K