Proving/Disproving: U and V Intersection in Rn

[jkm89]

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

If U, V are two subspaces of Rⁿ then U $$\cap$$ V $$\neq$$ $$\phi$$.

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

 

[rasmhop]

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

If U, V are two subspaces of Rⁿ then U $$\cap$$ V $$\neq$$ $$\phi$$.

I just want to make sure; $$\phi$$ 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
$$\phi \quad \emptyset$$
The first is phi and the second is "empty set".

See http://en.wikipedia.org/wiki/Empty_set#Notation" for a bit more information.

 

[pbandjay]

Compare
$$\phi \quad \emptyset$$
The first is phi and the second is "empty set".

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