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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

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# Proving that the intersection of any two intervals is an interval

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