# Abstract Geometry Proof

1. Aug 29, 2009

### ETuten

1. The problem statement, all variables and given/known data

Let {S1,L1} and {S2,L2} be abstract geomettries. If S=S1 ^ S2 and L=L1 ^ L2 prove that {S,L} is an abstract geometry ( where ^ = intersection)

2. Relevant equations

3. The attempt at a solution

Let {S1,L1} and {S2,L2} be abstract geometries. Assume that S=S1 ^ S2. Let x belong to S therfore by definiton of an intersection x belongs to S1 and x belongs to S2. Also assume that L=L1 ^ L2. Let y belong to L therefore by defintion of an intersection y belongs to L1 and y belongs to L2. Since {S1,L1} and {S2,L2} are abstract geometries {S,L} must also be an abstract geometry.

Now that I have typed all that I am not even sure that what I was trying to prove was possible. Am I even in the right ball park?

2. Aug 29, 2009

### Hurkyl

Staff Emeritus
I'm not familiar with the term "abstract geometry" -- could you define it?

3. Aug 30, 2009

### HallsofIvy

Staff Emeritus
Also, please understand that notation is not always universal. What is the definition of "abstract geometry", and what are S and L here?