Quantifiers - does this order matter?

  • Context: Graduate 
  • Thread starter Thread starter gmmstr827
  • Start date Start date
  • Tags Tags
    Matter
Click For Summary
SUMMARY

The discussion clarifies that the order of quantifiers in mathematical logic does not affect the meaning when using existential quantifiers. Specifically, the expressions \exists x, \exists y and \exists y, \exists x are equivalent. This conclusion contrasts with the interpretation of a professor who believes the order is significant, suggesting a misunderstanding of the principles of quantification in logic. The community consensus confirms that both expressions convey the same existential relationship.

PREREQUISITES
  • Understanding of existential quantifiers in logic
  • Familiarity with mathematical notation
  • Basic knowledge of logical expressions
  • Concept of quantifier order in predicate logic
NEXT STEPS
  • Research the laws of quantification in mathematical logic
  • Study the differences between existential and universal quantifiers
  • Explore predicate logic and its applications in formal proofs
  • Learn about the implications of quantifier order in logical statements
USEFUL FOR

Students of mathematics, logic enthusiasts, educators in mathematical logic, and anyone seeking to clarify the principles of quantification in formal logic.

gmmstr827
Messages
82
Reaction score
1
Is saying \existsx, \existsy
the same as saying \existsy, \existsx?
 
Physics news on Phys.org
Hi gmmstr827! :smile:

No, in this case, the order doesn't matter.
 
Alright, because the professor I have right now thinks those are two completely different things. He reads it as "there exists an x such that there exists a y (for that specific x)." This is the second time I had the class (it didn't transfer colleges) and my previous professor said they're the same thing.

Is there a law describing this somewhere?
 

Similar threads

Insights Brownian Motions and Quantifying Randomness in Physical Systems
  • · Replies 1 ·
Replies
1
Views
9K
Undergrad Is this the correct way to quantify these integers?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Does Organic Matter Experience Gravity on the Moon?
  • · Replies 15 ·
Replies
15
Views
2K
High School How do we know if a distant galaxy is matter or anti-matter?
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Proof of ##\cap_{i\in \cup F}A_i=\cap_{x\in F}(\cap_{i\in X}A_i)##?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Galactic collision and dark matter
  • · Replies 1 ·
Replies
1
Views
330
Undergrad How Does Vera Rubin's Research Support the Existence of Dark Matter in Galaxies?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad [Logic] Order of quantifiers and brackets
  • · Replies 24 ·
Replies
24
Views
3K
High School How can a black hole absorb matter?
  • · Replies 31 ·
2
Replies
31
Views
2K
Undergrad Matter Anti-Matter Annihilation
  • · Replies 4 ·
Replies
4
Views
3K