Calculating Diameters of Interval Unions

[julia89]

I know that the diameter for an interval [a,b] is defined as b-a

but what is
1. Diam of (-1,1]U(2,3)
2.Diam of (1,1/2)U(1/4,1/8)U(1/16,1/32)U...

Thanks

 

[Dick]

The diameter is defined as the diameter of the smallest interval that contains the set.

 

[HallsofIvy]

I know that the diameter for an interval [a,b] is defined as b-a

but what is
1. Diam of (-1,1]U(2,3)
2.Diam of (1,1/2)U(1/4,1/8)U(1/16,1/32)U...

Thanks

You obviously can't do that unless you know the definition of "diameter of a set or real numbers", not just the diameter of an interval. Fortunately, Dick has provided that.

 

[julia89]

so if i am right

1. Diam of (-1,1]U(2,3)=2+1=3
2.Diam of (1,1/2)U(1/4,1/8)U(1/16,1/32)U...=1/2+1/4+1/16+...

Is this correct?

 

[HallsofIvy]

The first one is correct, the second one is not. Did you notice that (1/4, 1/8), (1/16, 1/32), etc. are all SUBSETS of (1, 1/2)? What is (1,1/2)U(1/4,1/8)U(1/16,1/32)U...?