Examples of 'least element' in a sentence
Meaning of "least element"
least element - refers to the smallest or minimum component within a system or structure
How to use "least element" in a sentence
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least element
Meaning it has a least element and greatest element.
Polyhedral sets having a least element.
See least element.
The most basic example is given by the least element of a poset.
A cut with both a least element and a greatest element is called a jump.
Subset of X has a least element.
The least element of this lattice is the number 1, since it divides any other number.
Being the least element.
Bounded lattice, a lattice with a greatest element and least element.
A cut with neither a least element nor a greatest element is called a gap.
That is, every nonempty subset has a least element.
The least element of this lattice is 0, but no greatest element exists.
A well-order is linear order where every nonempty subset has a least element.
Ideally, a mapping also exists from every least element to every requirement and test.
For example, functions that preserve the empty supremum are those that preserve the least element.
See also
Complete lattices and orders with a least element ( the " empty supremum " ) provide further examples.
A lot is hidden here as well, Therefore it has a least element.
Since x is the least element of X, we.
More generally, Chomp can be played on any partially ordered set with a least element.
The least element of N is 0.
A linear order where every nonempty subset has a least element is called a well-order.
In another example, at least element 116 comprises a susceptor ( typically provided as a susceptor film ).
A principal ( or fixed, or trivial ) ultrafilter is a filter containing a least element.
Formally, an element m is a least element if, m ≤ a, for all elements a of the order.
However, this is not true, since is the least element in.
Its universe and least element are symbolized by U and ∅ { \ displaystyle \ varnothing }, respectively.
Every non-empty well-ordered set has a least element.
It is denoted 0 ( zero ) because it is the least element of the poset formula 1.
Suppose there exists a non-empty set, S, of naturals that has no least element.
For example, what about a function that finds the least element in a list?
Let I be a bounded lattice with greatest element 1 and least element 0.
What we have already proved, 1 is the least element of N.
But,, and this contradicts the fact that is the least element in.
So by well-ordering, S has a least element r.
By the Well-Ordering Principle, T has a least element m.
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