The infimum is the greatest lower bound of a set S, defined as a quantity m such that no member of the set is less than m, but if ϵ is any positive quantity, however small, there is always one member that is less than m + ϵ. When it exists (which is not required by this definition, e.g., inf R does not exist), the infimum is denoted inf S or inf_(x element S) x. The infimum is implemented in the Wolfram Language as MinValue[f, constr, vars]. Consider the real numbers with their usual order. Then for any set M⊆R, the infimum inf M exists (in R) if and only if M is bounded from below and nonempty.
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