Let S := {x ∈ R : x > 0}. Find inf S
Question
Let S := {x ∈ R : x > 0}. Find inf S
Solution
The set S is defined as all real numbers x that are greater than 0.
The infimum (inf) of a set is the greatest number that is less than or equal to all numbers in the set.
Since the set S includes all real numbers greater than 0, there is no real number that is less than or equal to all numbers in the set.
However, in the context of extended real number system, where we include negative infinity (-∞) and positive infinity (∞), the infimum of S would be 0, because 0 is the greatest number that is less than all positive real numbers.
So, inf S = 0.
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