- #1

- 79

- 12

Prove that if I

_{1}, I

_{2}are intervals and J = I

_{1}[itex]\cap[/itex]I

_{2}then J is an interval.

To be honest I don't even know where to start. There's a "hint" that suggests that I first write out the definitions of I

_{1}, I

_{2}, J as intervals and of the intersection between I

_{1}and I

_{2}, but that hasn't really enlightened me...

So I just have:

A subset I

_{n}of ℝ is an interval if [itex]\forall[/itex] x,y,z [itex]\in[/itex] ℝ , x[itex]\in[/itex]I

_{n}, z[itex]\in[/itex]I

_{n}and x<y<z then y[itex]\in[/itex]I

_{n}(I used n instead of 1 and 2 because I am too lazy to write it out twice. Also, substitute J in as appropriate xD )

I

_{1}[itex]\cap[/itex]I

_{2}= {x: x[itex]\in[/itex]I

_{1}and x[itex]\in[/itex]I

_{2}}

I don't know where to go from there basically. If someone could even so much as nudge me in the right direction I would be very appreciative :D