i need again some help here. i am defining the minimum and max and inf and sup of this set
$A:=(]1,2[ \cup ]2,3]) \cup \{2\}$ which is equal to the interval $(1,3]$
i say, max is 3, and sup is also 3. and 1 is inf but what is minimum? there are many numbers with $1
can someone help me to understand the intuitive notion of infimum,supremum, and minimum and maximum. i know that the number which is minimum and maximum must be contained in the set. and every bounded non-empty set has supremum and infimum, but not always minimum and maximum. so in my case, there are maximum, supremum and inf, but no minimum? am i right?