What does sup mean in stats?
The supremum (abbreviated sup; plural suprema) of a subset of a partially ordered set is the least element in that is greater than or equal to all elements of if such an element exists. Consequently, the supremum is also referred to as the least upper bound (or LUB).
What is meant by sup and inf?
The supremum of a set is its least upper bound and the infimum is its greatest upper bound. Definition 2.2. Suppose that A ⊂ R is a set of real numbers.
How do you find sup and inf?
To find a supremum of one variable function is an easy problem. Assume that you have y = f(x): (a,b) into R, then compute the derivative dy/dx. If dy/dx>0 for all x, then y = f(x) is increasing and the sup at b and the inf at a. If dy/dx<0 for all x, then y = f(x) is decreasing and the sup at a and the inf at b.
What is the difference between sup and Max?
A maximum is the largest number WITHIN a set. A sup is a number that BOUNDS a set. A sup may or may not be part of the set itself (0 is not part of the set of negative numbers, but it is a sup because it is the least upper bound).
What is greatest lower bound example?
If the set has the smallest element, then the greatest lower bound of the set is the same as the smallest element; however, if the set does not have the smallest element, then it is a little trickier. Let us look at the following example. S={11,12,13,14,15,16,…} .
What is LUB and GLB?
– least upper bound (lub) is an element c such that. a · c, b · c, and 8 d 2 S . ( a · d Æ b · d) ) c · d. – greatest lower bound (glb) is an element c such that. c · a, c · b, and 8 d 2 S . (
How is INF calculated?
INF is the result of a numerical calculation that is mathematically infinite, such as: 1/0 → INF. INF is also the result of a calculation that would produce a number larger than 1.797 x10+308 , which is the largest floating point number that Analytica can represent: 10^1000 → INF.
Can a set have a maximum but no supremum?
In particular, if a set has both a supremum and a maximum, then they are the same element. The set may also have neither a supremum nor a maximum (e.g., the rationals as a subset of the reals). But if it has only one them, then it has a supremum which is not a maximum and is not in the set.
What is the maximum of the set?
The maximum is a unique number for a given set of data. This number can be repeated, but there is only one maximum for a data set. There cannot be two maxima because one of these values would be greater than the other.
What is greatest lower bound math?
a lower bound that is greater than or equal to all the lower bounds of a given set: 1 is the greatest lower bound of the set consisting of 1, 2, 3. Abbreviation: glb. Also called infimum.
Is the poset Z+ /) a lattice?
There is no glb either. The poset is not a lattice. We impose a total ordering R on a poset compatible with the partial order.