Q: Formula for Partially ordered set for n elements?

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An antichain is a subset of a partially ordered set such that any two elements in the subset are incomparable.

They are the elements from the first set in the original Carestian product. For example, if you make ordered pairs on an x-y plane, then they are the elements of the set X.

It is called an ordered pair.

it denotes the set of ordered pairs with elements of A and b in the format (a,b)

If the set has n elements, the number of subsets (the power set) has 2n members.

Related questions

An antichain is a subset of a partially ordered set such that any two elements in the subset are incomparable.

If {X,R} is a Partially Ordered Set, then {X,R(inverse)} is also a Partially Ordered Set.

They are the elements from the first set in the original Carestian product. For example, if you make ordered pairs on an x-y plane, then they are the elements of the set X.

They are elements of the infinite set of ordered pairs of the form (x, 0.1x+1). It is an infinite set and I am not stupid enough to try to list its elements!

A join and meet are binary operations on the elements of a POSET, or partially ordered set. A join on a set is defined as the supremum with respect to a partial order on the set, provided it exists. A meet on a set is defined either as the unique infimum with respect to the partial order imposed on the set, if the infimum exists.

It is called an ordered pair.

they are the first set of paired elements

Since relation is a set, and tuples are element of a set, according to set theory, the elements of a set are not ordered.

it denotes the set of ordered pairs with elements of A and b in the format (a,b)

It is a partially ordered set. That means it is a set with the following properties: a binary relation that is 1. reflexive 2. antisymmetric 3. transitive a totally ordered set has totality which means for every a and b in the set, a< or equal to b or b< or equal to a. Not the case in a poset. So a partial order does NOT have totality.

If there is an odd number of elements in the set, then it is the median. If there is an even number, then there is no middle number.

If the set has n elements, the number of subsets (the power set) has 2n members.