empty multiset

USAGE SUMMARY

The phrase "empty multiset" is correct and usable in written English.
It can be used in mathematical or computer science contexts to refer to a multiset that contains no elements. Example: "In set theory, an empty multiset is often denoted by the symbol ∅."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

3 human-written examples

The empty multiset is denoted by empty.

Complex & Intelligent Systems

We shall denote an empty multiset (langle emptyset,frangle ) as (emptyset ) and we shall abbreviate a multiset ((T^k)) to (T^k) and (T^1) to (T).

Vietnam Journal of Computer Science

The empty multiset, based on ss, is composed of pairs of elements of the support set related to 0. Thus, it is a total function, which for each element of the starting set combines the integer 0: mathrm{Ms}_mathrm{empty} left(mathrm{ss}right)==left{mathrm{elt} | mathrm{elt}:mathrm{ss}times left{0right}right}.

European Transport Research Review

Human-verified similar examples from authoritative sources

Similar Expressions

57 human-written examples

A sequence of multisets (mathcal {T}) may contain one or more empty multisets.

Vietnam Journal of Computer Science

Let (M_+), (N_+) range over non-empty sets of sibling membranes, (M_i) over membranes, (M_*), (N_*) range over possibly empty multisets of sibling membranes, and L over labels.

Complex & Intelligent Systems

A workload trace of a sequence of multisets (mathcal {T}) starting at the (k -th time unit, (1 le k -th|U|-|matimel {T}|+1) and spreading over (|unittime units is denoted by (W_{mathcal {T}_k}) and it is defined as a sequence of multisets (mathcal {T}) extended on the left with (k-1) empty sets and on the right with (|U|-k-|mathcale{T}|+1) empty multisets.

Vietnam Journal of Computer Science

A directed hypergraph is a set V of vertices and a set E of hyperarcs, where each hyperarc (e=(T e), H e))) is an ordered pair of non-empty multisets of vertices.

Journal of Cheminformatics

A multiset m such that dom((m) = emptyset ) is called empty and is denoted with (emptyset ), with abuse of notation.

Vietnam Journal of Computer Science

Empty, empty.

The New Yorker

Empty bottles.

The New Yorker

That Margaret will feel empty, empty, empty".

The New York Times

Expert writing Tips

Best practice

When discussing mathematical concepts, ensure the use of "empty multiset" is appropriate for the context. Multisets allow for duplicate elements, so an empty multiset specifically means there are no elements at all, not just no unique elements.

Common error

Avoid interchanging "empty multiset" with the concept of an empty set when the specific properties of a multiset are relevant. An empty set can be a member of a multiset, but an "empty multiset" contains nothing at all.

Linguistic Context

The phrase "empty multiset" functions as a noun phrase, specifically referring to a multiset that contains no elements. According to Ludwig, the phrase is correct and usable in written English, especially in mathematics or computer science contexts.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Wiki

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Ludwig's WRAP-UP

The term "empty multiset" refers to a multiset that contains no elements, primarily used in mathematical and computer science contexts. Ludwig AI confirms its correctness and usability in these fields. While the phrase is grammatically sound, it's relatively rare, primarily appearing in scientific publications. Alternatives like "null multiset" or "zero multiset" may be used depending on the specific context. It's crucial to distinguish "empty multiset" from related concepts like the empty set, especially when the multiplicity of elements is a key consideration.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

null multiset

Replaces "empty" with its synonym "null", maintaining the precise mathematical meaning.

zero multiset

Employs "zero" to convey the concept of having no elements in the multiset.

multiset with no elements

Expresses the concept using a more descriptive phrase.

multiset of cardinality zero

Replaces "empty" with a formal mathematical description using cardinality.

vacuous multiset

Uses "vacuous" which implies emptiness or lack of content.

devoid multiset

Replaces empty with devoid, to indicate that a multiset is lacking elements.

multiset containing no elements

Explicitly states that the multiset does not contain any elements.

a multiset with an empty domain

Focuses on the domain of the multiset being empty, thus implying an empty multiset.

multiset with zero multiplicity for all elements

Describes the multiset by stating each element has a multiplicity of zero.

tautologically empty multiset

Uses "tautologically" to emphasize the self-evident emptiness of the multiset.

FAQs

What is the difference between an "empty multiset" and an empty set?

An "empty multiset" is a multiset that contains no elements. An empty set, on the other hand, is a set that contains no elements. The key difference is that multisets allow for multiple instances of the same element, while sets do not. Even with that said, both are empty, but they refer to different mathematical structures.

How is an "empty multiset" denoted?

An "empty multiset" is often denoted by symbols similar to those used for the empty set, such as ∅ or {}. The specific notation may depend on the context or the author's preference.

In what contexts would I use the term "empty multiset"?

You'd typically use "empty multiset" in mathematical or computer science contexts where multisets are relevant. This includes areas like combinatorics, algorithm analysis, and formal language theory, where you need to explicitly handle collections that may contain duplicate elements but can also be entirely devoid of any elements.

What are some alternative phrases for "empty multiset"?

You can use alternatives like "null multiset" or "zero multiset", depending on the level of formality and the specific nuance you wish to convey. These alternatives maintain the accurate meaning of a multiset with no elements.