# Infimum

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A Infimum is the Set Element of a Partially Ordered Set that is GreaterThanOrEqualTo all Set Elements of some Subset of the set.

**AKA:**Infima, Greatest Lower Bound, GLB.- …

**Counter-Example(s):**- a Supremum.

**See:**Numeric Interval, Lattice, Conceptual Graph.

## References

### 2009

- http://en.wikipedia.org/wiki/Infimum
- In mathematics, particularly set theory, the
**infimum**(plural infima) of a subset of some set is the greatest element (not necessarily in the subset) that is less than or equal to all elements of the subset. Consequently the term**greatest lower bound**(also abbreviated as glb**or**GLB) is also commonly used. Infima of real numbers are a common special case that is especially important in analysis. However, the general definition remains valid in the more abstract setting of order theory where arbitrary partially ordered sets are considered. - Infima are in a precise sense dual to the concept of a supremum and thus additional information and examples are found in that article.
- In analysis the infimum or greatest lower bound of a subset [math]\displaystyle{ S }[/math] of real numbers is denoted by inf(
*S*) and is defined to be the biggest real number that is smaller than or equal to every number in*S*. If no such number exists (because [math]\displaystyle{ S }[/math] is not bounded below), then we define inf(*S*) = −∞. If [math]\displaystyle{ S }[/math] is empty, we define inf(*S*) = ∞ (see extended real number line).

- In mathematics, particularly set theory, the

### 2008

- (Corbett, 2008) ⇒ Dan R. Corbett. (2008). “Graph-based Representation and Reasoning for Ontologies.” In: Studies in Computational Intelligence, Springer. [http://dx.doi.org/10.1007/978-3-540-78293-3 10.1007/978-3-540-78293-3 doi:[http://dx.doi.org/10.1007/978-3-540-78293-3 10.1007/978-3-540-78293-3)
- The greatest lower bound (GLB) of two CGs is the most general common specialization of the two conceptual graphs. Let G" be a specialization of G and G'. G" is the GLB of G and G' if, for any conceptual graph U where G ∨ G' = U, either G" ≥ U or G" = U.
- The GLB of two graphs s and t is written as s | | t. Conversely, the most specific common generalization, known as the least upper bound (LUB), of two graphs is written s |_| t. Note that it is not always possible to find a unique GLB. In these instances, it is often the case that a greedy algorithm is used which picks the first G" which matches the constraints.