#What is the formal definition of max and min function on a finite/countable set of real numbers?

9 messages · Page 1 of 1 (latest)

buoyant viper
#

I can only think of defining max (min should be able to look analoguesly) recursevely:
For a finite set of real numbers X = {a1, a2, a3, ... , an}
If |X| = 1 then max X = a1
If |X| = 2 then max X = (a1 + a2 + |a2 - a1|)/2
If |X| = n then max X = max { max( X \ {an}, an }

For a countable set I don't have an idea how I could do this since it is possible for a countable set NOT to have a max/min value (i.e. N or Z )

ionic hearthBOT
#
  1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
  2. Wait patiently for a helper to come along.
  3. Once someone helps you, say thank you and close the thread with:
    +close
  4. Feel free to nominate the person for helper of the week in #helper-nominations
  5. Do not ping the mods, unless someone is breaking the rules.
  6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:
fossil tide
#

you generalize it to sup/inf as any day1 of a real analysis course tells you, to which the sup and inf always exist (taking values in [-inf,inf])

buoyant viper
#

Thanks

fossil tide
#

I just stated the obvious for you cause you seemed to ignore it

#

but yw ig

buoyant viper
#

+close