Given any distinct points (x1,x2,x3,x4) in RP1 prove that they form a h ar-m onic division, i.e.,[x1,x2,x3,x4]=−1 iff Prove that [0,x2,x3,x4] =−1 iff Prove that [x1,x2,x3,∞] = − 1 iff 2x3 = x1 +...

Given any distinct points (x1,x2,x3,x4) in RP1 prove that they form a h ar-m onic division, i.e.,[x1,x2,x3,x4]=−1 iff

Prove that [0,x2,x3,x4] =−1 iff

Prove that [x1,x2,x3,∞] = − 1 iff

2x3 = x1 + x2.

Do the above results extend to P1K where K is any field?