Proving/Disproving: U and V Intersection in Rn

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SUMMARY

The discussion centers on the proof or disproof of the statement regarding the intersection of two subspaces U and V in Rn, specifically that U ∩ V ≠ ∅ (the empty set). Participants clarify that the symbol φ represents the Greek letter phi, while ∅ denotes the empty set. The distinction between φ and ∅ is emphasized, with a reference to Wikipedia for further clarification on notation.

PREREQUISITES
  • Understanding of vector spaces and subspaces in Rn
  • Familiarity with set theory, particularly the concept of the empty set
  • Knowledge of mathematical notation, including Greek letters and symbols
  • Basic proof techniques in linear algebra
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  • Research the properties of vector space intersections
  • Study the implications of U and V being subspaces of Rn
  • Learn about the notation and usage of Greek letters in mathematics
  • Explore examples of proving intersections in linear algebra
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Students of linear algebra, mathematicians, and educators looking to deepen their understanding of vector spaces and set notation.

jkm89
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So for my homework I have to prove (or disprove) this statement:

If U, V are two subspaces of Rn then U [tex]\cap[/tex] V [tex]\neq[/tex] [tex]\phi[/tex].

I just want to make sure; [tex]\phi[/tex] is the null set right? The set with nothing in it?
 
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jkm89 said:
So for my homework I have to prove (or disprove) this statement:

If U, V are two subspaces of Rn then U [tex]\cap[/tex] V [tex]\neq[/tex] [tex]\phi[/tex].

I just want to make sure; [tex]\phi[/tex] is the null set right? The set with nothing in it?

Yes it's the empty set. However the symbol isn't the greek letter phi, but a symbol of its own based on the letter Ø (a letter in some alphabets).

Compare
[tex]\phi \quad \emptyset[/tex]
The first is phi and the second is "empty set".

See http://en.wikipedia.org/wiki/Empty_set#Notation" for a bit more information.
 
Last edited by a moderator:
rasmhop said:
Compare
[tex]\phi \quad \emptyset[/tex]
The first is phi and the second is "empty set".

This is why I got used to writing [tex]\varphi[/tex] for phi. Although I never learned if there is a proper time to use [tex]\phi[/tex] and a proper time to use [tex]\varphi[/tex].
 

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