Bounded Intervals

  • Thread starter Icebreaker
  • Start date
  • #1
Icebreaker
"If I and J are bounded, then I[tex]\cap[/tex]J is also bounded."

Now, I was able to do this using the definition of suprema and infima and so fourth, but it is one godawful mess. I could sumbit it as is, but I was wondering if there's an easier way.
 

Answers and Replies

  • #2
695
0
Why would you involve suprema and infima?

Let C be an upper bound of I, and D an upper bound of J. Then max{C, D} is an upper bound of [tex]I \cap J[/tex]. Similarly for the lower bound.
 

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