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Summation where the number of terms is zero
an empty sum, or nullary sum, is a summation where the number of terms is zero. The natural way to extend non-empty sums is to let the empty sum be the
Empty_sum
Mathematical set containing no elements
one is inevitably led to the convention that the sum of the elements of the empty set (the empty sum) is zero. The reason for this is that zero is the
Empty_set
Figurate number
the tetrahedral numbers. Taking T 0 = 0 {\displaystyle T_{0}=0} (see empty sum), the first few terms are 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66,
Triangular_number
Inverse of a finite difference
{\displaystyle \sum _{\nu =x}^{y}(\lambda f(\nu )+\mu g(\nu ))=\lambda \sum _{\nu =x}^{y}f(\nu )+\mu \sum _{\nu =x}^{y}g(\nu )} . Empty Sum Condition: ∑
Indefinite_sum
Result from multiplying no factors
one), just as the empty sum — the result of adding no numbers — is by convention equal to the additive identity (zero). The term empty product is most often
Empty_product
Addition of several numbers or other values
addends or summands; the result is their sum or total. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials
Summation
Problem in computer science
that the sum ∑ x = i j A [ x ] {\displaystyle \sum _{x=i}^{j}A[x]} is as large as possible. (Some formulations of the problem also allow the empty subarray
Maximum_subarray_problem
Decomposition of an integer as a sum of positive integers
3 + 1 2 + 2 2 + 1 + 1 1 + 1 + 1 + 1 The only partition of zero is the empty sum, having no parts. The order-dependent composition 1 + 3 is the same partition
Integer_partition
Topics referred to by the same term
contracting tensor indices Empty sum, a sum with no terms Indefinite sum, the inverse of a finite difference Kronecker sum, an operation considered a
Sum
Aircraft weight without fuel or payload
Empty weight (EW) is the sum of the ‘as built’ manufacturer's empty weight (MEW), plus any standard items (SI) plus any operator items (OI), EW = MEW
Operating_empty_weight
Number
method, such as l'Hôpital's rule. The sum of 0 numbers (the empty sum) is 0, and the product of 0 numbers (the empty product) is 1. The factorial 0! evaluates
0
Canadian rock band
Sum 41 was a Canadian rock band formed in Ajax, Ontario, in 1996. The band's final lineup consisted of Deryck Whibley (lead vocals, rhythm guitar, keyboards)
Sum_41
sum _{i}x_{i}&&=\sum _{i}\tan \theta _{i}\\[6pt]e_{2}&=\sum _{i<j}x_{i}x_{j}&&=\sum _{i<j}\tan \theta _{i}\tan \theta _{j}\\[6pt]e_{3}&=\sum
List of trigonometric identities
List_of_trigonometric_identities
In linear algebra, generated subspace
empty, the only possibility is n = 0, and the previous expression for span ( S ) {\displaystyle \operatorname {span} (S)} reduces to the empty sum.
Linear_span
Mathematical form
The empty product on numbers and most algebraic structures has the value of 1 (the identity element of multiplication), just like the empty sum has the
Product_(mathematics)
Chinese cuisine
Dim sum (traditional Chinese: 點心; simplified Chinese: 点心; pinyin: diǎn xīn; Jyutping: dim2 sam1) is a large range of small Chinese dishes that are traditionally
Dim_sum
Conditional statement which is true because the antecedent cannot be satisfied
{\displaystyle \forall x\,P(x)\equiv \neg \exists x\,\neg P(x)} Empty sum and empty product Empty function Paradoxes of material implication, especially the
Vacuous_truth
Infinite sum
of these sums exist via the completeness of the real numbers and whether series terms can be rearranged or not without changing their sums using absolute
Series_(mathematics)
Special functions of several complex variables
topics such as number theory: "in how many ways can a number be written as a sum of squares?" physics: "how does heat flow on a toroidal ring?", "how do quantum
Theta_function
Mathematical approximation of a function
infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its
Taylor_series
Data structure
indices corresponding to sums of k {\displaystyle k} distinct powers of 2 (with k = 0 {\displaystyle k=0} representing an empty sum 0). For example, level
Fenwick_tree
Sums vector sets A and B by adding each vector in A to each vector in B
of radius 0 is the empty set). The Minkowski sum of a closed ball and an open ball is an open ball. More generally, the Minkowski sum of an open subset
Minkowski_addition
In type theory, a type with no terms
In type theory, an empty type or absurd type, typically denoted 0 {\displaystyle \mathbb {0} } is a type with no terms. Such a type may be defined as
Empty_type
(origin) belongs to all conical hulls (since the summation becomes an empty sum). The conical hull of a set S {\displaystyle S} is a convex set. In fact
Conical_combination
Finite sets whose elements are all hereditarily finite sets
f(a)=\sum _{b\in a}2^{f(b)}} For example, the empty set { } {\displaystyle \{\}} contains no members, and is therefore mapped to an empty sum, that is
Hereditarily_finite_set
Node ordering for directed acyclic graphs
a set S; at least one such node must exist in a non-empty (finite) acyclic graph. Then: L ← Empty list that will contain the sorted elements S ← Set of
Topological_sorting
Special type of continuous-time Markov process
{1}{n}}+{\frac {1}{n}}\sum _{k=1}^{K-1}{\frac {1}{\prod _{j=1}^{k}\ln _{(j)}(n)}}+{\frac {c}{n\prod _{j=1}^{K}\ln _{(j)}(n)}},} where the empty sum for K = 1 {\displaystyle
Birth–death_process
Numbers obtained by adding the two previous ones
mathematics, the Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci
Fibonacci_sequence
Topics referred to by the same term
Joyce Carol Oates Empty sum Non Zero Sumness Zerosumfree monoid This disambiguation page lists articles associated with the title Zero sum. If an internal
Zero_sum_(disambiguation)
1994 film by Kevin Dowling
Australia The Sum of Us at Box Office Mojo www.imdb.com https://www.imdb.com/title/tt0111309/. Retrieved 14 May 2026. {{cite web}}: Missing or empty |title=
The_Sum_of_Us_(film)
Type of figurate number
− 1 ( 4 k + 1 ) {\displaystyle h_{n}=\sum _{k=0}^{n-1}{(4k+1)}} where the empty sum is taken to be 0. The sum of the reciprocal hexagonal numbers is
Hexagonal_number
2026 film by Joe Carnahan
broken down as team members suspect each other of trying to steal a large sum of cash. It was released by Netflix on January 16, 2026, to generally favorable
The_Rip_(film)
Decision problem in computer science
The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers
Subset_sum_problem
Number of partitions of an integer
convention p(0) = 1, as there is one way of representing 0 as a sum of positive integers (the empty sum). Furthermore p(n) = 0 when n is negative. The first few
Partition function (number theory)
Partition_function_(number_theory)
Type of vector space in math
n {\displaystyle \sum _{n=0}^{\infty }\mathbf {x} _{n}} consisting of vectors in R3 is absolutely convergent provided that the sum of the lengths converges
Hilbert_space
On the unique representation of integers as sums of non-consecutive Fibonacci numbers
representation of integers as sums of Fibonacci numbers. It states that every positive integer can be represented uniquely as the sum of one or more distinct
Zeckendorf's_theorem
Algebra of formal sums
combination of zero basis elements, according to the usual convention for an empty sum, and it must not be possible to find any other combination that represents
Free_abelian_group
Data type defined by combining other types
data type is the singly linked list. A list type is a sum type with two variants, Nil for an empty list and Cons x xs for the combination of a new element
Algebraic_data_type
This is a list of episodes for the American television sitcom Empty Nest, a spinoff of The Golden Girls that originally aired on NBC from October 8, 1988
List_of_Empty_Nest_episodes
Mathematical theorem
For n = 0 this is just the assumed integral inequality, because the empty sum is defined as zero. Induction step from n to n + 1: Inserting the assumed
Grönwall's_inequality
Sequence of equally spaced numbers
arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series. According
Arithmetic_progression
Finger-counting system
hour using 4 fingers (1-12) and the minutes using 6 fingers (0-59). 0 = empty sum 1 = 1 2 = 2 4 = 4 6 = 4 + 2 7 = 4 + 2 + 1 14 = 8 + 4 + 2 16 = 16 19 =
Finger_binary
Numeric quantity representing the center of a collection of numbers
purpose. The arithmetic mean, also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set
Mean
2021 studio album by Tantric
The Sum of All Things is the eighth full-length studio album released by the American rock band Tantric. The album was released on July 23, 2021 via Cleopatra
The_Sum_of_All_Things
Theorem in set theory
index set I is finite. If I is empty, then the left sum is the empty sum and therefore 0, while the right product is the empty product and therefore 1.) Kőnig's
Kőnig's_theorem_(set_theory)
Determinant of a product of rectangular matrices
{[n]}{m}}} is the empty set, and the formula says that det ( A B ) = 0 {\displaystyle \det(AB)=0} (its right hand side is an empty sum); indeed in this
Cauchy–Binet_formula
American actor (1954–2026)
Streak" as Don Gibb Secret Agent Man Buff Bobby Barnett 1 Episode: "WhupSumAss" Early Edition Odessa "Stumpy" McNeil 1 Episode: "Mel Schwartz, Bounty
Donald_Gibb
Chinese martial artist (1893–1972)
they had several children: sons Ip Chun and Ip Ching, and daughters Ip Nga-sum (葉雅心) and Ip Nga-wun (葉雅媛).[additional citation(s) needed] During the Second
Ip_Man
2001 single by Sum 41
"In Too Deep" is a song by Canadian rock band Sum 41. It is the seventh track on their debut studio album All Killer No Filler (2001), and was released
In_Too_Deep_(Sum_41_song)
Generalizations of '"`UNIQ--math-00000046-QINU`"' in algebraic structures
(f+g)(x)=f(x)+g(x)} The empty set under set union An empty sum or empty coproduct An initial object in a category (an empty coproduct, and so an identity
Zero_element
Criterion for the convergence of a series
{1}{n}}\sum _{i=1}^{K-1}{\frac {1}{\prod _{k=1}^{i}\ln _{(k)}(n)}}+{\frac {\rho _{n}}{n\prod _{k=1}^{K}\ln _{(k)}(n)}},\quad K\geq 1.} (The empty sum is assumed
Ratio_test
Theorem of convex functions
log ( x i ) n {\displaystyle \log \!\left({\frac {\sum _{i=1}^{n}x_{i}}{n}}\right)\geq {\frac {\sum _{i=1}^{n}\log \!\left(x_{i}\right)}{n}}} exp ( log
Jensen's_inequality
Function related to statistics and probability theory
log-likelihood, given no event, is 0, which corresponds to the value of the empty sum: without any data, there is no support for any models. The graph of the
Likelihood_function
Natural number between 89 and 91
dividing a set of six objects into three non-empty subsets. 90 is also the sixteenth Perrin number from a sum of 39 and 51, whose difference is 12. The members
90_(number)
Basic integral in elementary calculus
finite sums of areas of vertical rectangles. For suitable functions, including every continuous function on a closed bounded interval, these Riemann sums approach
Riemann_integral
Hong Kong actor, martial artist, and singer (born 1975)
directed by Stephen Chow: as the goalkeeper "Empty Hand" in Shaolin Soccer (2001) and as the Axe Gang boss Brother Sum in Kung Fu Hustle (2004). In 2008, due
Danny_Chan_Kwok-kwan
Natural number
into 3 non-empty sets. 301 is the sum of consecutive primes 97, 101, and 103. 301 is a happy number, meaning that infinitely taking the sum of the squares
301_(number)
In geometry, set whose intersection with every line is a single line segment
finite collection of non-empty sets: Conv ( ∑ n S n ) = ∑ n Conv ( S n ) . {\displaystyle {\text{Conv}}\left(\sum _{n}S_{n}\right)=\sum _{n}{\text{Conv}}\left(S_{n}\right)
Convex_set
Criterion for the convergence of an infinite series
{1}{n}}+{\frac {1}{n}}\sum _{i=1}^{K-1}{\frac {1}{\prod _{k=1}^{i}\ln _{(k)}(n)}}+{\frac {\rho _{n}}{n\prod _{k=1}^{K}\ln _{(k)}(n)}}.} (The empty sum is assumed
Root_test
Musical comedy drama February 13, 2026 1 season, 8 episodes Pending Maa Ka Sum Drama April 3, 2026 1 season, 8 episodes Pending Matka King Historical crime
List of Amazon Prime Video original programming
List_of_Amazon_Prime_Video_original_programming
Description of flat one-vertex origami
partial alternating sum α1 − α2 + α3 − ⋯ + α2i − 1 − α2i is as small as possible. Either i = 0 and the partial sum is an empty sum that is also zero, or
Kawasaki's_theorem
Brazilian footballer (born 1992)
5 million), with Neymar's parents confirmed to have received a €40 million sum. In the aftermath, Barcelona and Bartomeu were charged with tax fraud. Neymar
Neymar
Agent-based segregation model
fraction of neighbors B {\displaystyle B} that matches their group—ignoring empty spaces—is greater than or equal to B a {\displaystyle B_{\textrm {a}}}
Schelling's model of segregation
Schelling's_model_of_segregation
Bet sizing formula for long-term growth
{\sum _{k\notin S}p_{k}}{\left(D-\sum _{k\in S}\beta _{k}\right)}}.} One may prove that R ( S o ) = 1 − ∑ i ∈ S o f i o {\displaystyle R(S^{o})=1-\sum _{i\in
Kelly_criterion
Arithmetic operation
Dedekind cut of rationals: a non-empty set of rationals that is closed downward and has no greatest element. The sum of real numbers a and b is defined
Addition
(Mathematical) ring with a unique maximal ideal
then it has a term that is a unit (this says in particular that the empty sum cannot be a unit, so it implies 1 ≠ 0). If these properties hold, then
Local_ring
American singer-songwriter (born 1941)
so that no definitive or ideal version exists. Dylan's legacy will be the sum of thousands of performances, over many decades ... Every night, whether
Bob_Dylan
Abstract algebra concept
\mathbb {N} _{>0}} . However, the integer 0 can not be expressed as a (non-empty) sum of 1s, thus {1} is not a semigroup generator of the natural numbers. Similarly
Generating_set_of_a_group
The Neapolitan sums (Polish: Sumy neapolitańskie) refers to a loan made in 1557 by Bona Sforza, dowager Queen of Poland and Grand Duchess of Lithuania
Neapolitan_sums
Category-theoretic construction
In category theory, the coproduct, or categorical sum, is a construction which includes as examples the disjoint union of sets and of topological spaces
Coproduct
Rational number equal to an integer plus 1/2
{\displaystyle n} is odd. This includes n = 0 {\displaystyle n=0} since the empty sum 0 is not half-integer. The negative of a half-integer is a half-integer
Half-integer
integer partitions of 45 in which are empty or have smallest part not dividing the other ones 1068 = number that is the sum of 7 positive 5th powers, total
1000_(number)
Mathematical theory of data types
intersection. The sum type is written as either + {\displaystyle +} or ⊔ {\displaystyle \sqcup } . In programming languages, sum types may be referred
Type_theory
Algebraic structure in linear algebra
a vector space V is a non-empty subset of V that is closed under vector addition and scalar multiplication; that is, the sum of two elements of W and the
Vector_space
Film by Matt Bettinelli-Olpin and Tyler Gillett
set ablaze, and Grace is attacked by Becky, who she knocks out with her empty gun. Alex escapes his restraints to find Grace attacking his mother with
Ready_or_Not_(2019_film)
Decision rule used for minimizing the possible loss for a worst-case scenario
maximize the minimum gain. Originally formulated for several-player zero-sum game theory, covering both the cases where players take alternate moves and
Minimax
Association of one output to each input
called the empty function, or empty map, from the empty set to X. The graph of an empty function is the empty set. The existence of empty functions is
Function_(mathematics)
Algorithm for statistical inference on graphical models
Belief propagation, also known as sum–product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian
Belief_propagation
1978 single by Jackson Browne
"Running on Empty" is a song by American singer-songwriter Jackson Browne. It is the title track of his 1977 live album of the same name, recorded at
Running_on_Empty_(song)
King of Macedon from 336 to 323 BC
prosperity during Alexander's campaign in Asia. Alexander sent back vast sums from his conquest, which stimulated the economy and increased trade across
Alexander_the_Great
but identification with any of the three series is possible (unless the empty rime /ɨ/ is identified with /i/, in which case the velars become the only
Standard_Chinese_phonology
Complexity class
salesman problem—is NP-hard. The subset sum problem is another example: given a set of integers, does any non-empty subset of them add up to zero? That is
NP-hardness
scarlet red. In Poland, school grades range from 1 (worst) to 6 (best). Sum of individual polling results of the following parties: Coalition Civic
Opinion polling for the next Polish parliamentary election
Opinion_polling_for_the_next_Polish_parliamentary_election
2019 single by the Weeknd
the most time totaled in the Hot 100's top three, 21 weeks, equaling the sums of The Chainsmokers' "Closer" and Mark Ronson's "Uptown Funk!". For a short
Blinding_Lights
2016 film by Martin Scorsese
(1988) and Kundun (1997), and it feels like a self-conscious masterpiece, a summing-up from a filmmaker who, at 74, may be thinking of his legacy." Joshua
Silence_(2016_film)
Word processor
"averages" each sentence by adding the scores of its words and dividing the sum by the number of words in the sentence – the higher the average, the higher
Microsoft_Word
Gambling card game
by Charles Van-Tenac. Later, Chemin de Fer emerged as a two-player zero-sum game from Baccarat Banque. Chemin de Fer is a version which first appeared
Baccarat
2023 film by Greta Gerwig
and raw, untrammeled commercialism", applauded the production design, and summed: "The crucial partnership here is the one between director and performer
Barbie_(film)
English singer-songwriter (born 1991)
com/news/ni63961465/. Retrieved 14 April 2026. {{cite web}}: Missing or empty |title= (help) Petridis, Alex (18 November 2019). "Grounded: how Ed Sheeran
Ed_Sheeran
Indian film series
smuggling syndicate in the late 1990s. He starts out working for a small sum, but dreams of a better life. Pushpa franchise is the Fourth-highest-grossing
Pushpa_(film_series)
American actress
'PERFECT PARTY,' NEW GURNEY COMEDY". New York Times. Retrieved April 1, 2024. "Sum of Us, The". Williamstown Theatre Festival. Retrieved April 1, 2024. Debra
Debra_Mooney
Set of elements common to all of some sets
{\displaystyle A\cap B=B\cap A.} The intersection of any set with the empty set results in the empty set; that is, that for any set A {\displaystyle A} , A ∩ ∅ =
Intersection_(set_theory)
Statistical measure to determine how suited data is for factor analysis
{\underset {j\neq k}{\sum \sum }}r_{jk}^{2}}{\displaystyle {\underset {j\neq k}{\sum \sum }}r_{jk}^{2}+{\underset {j\neq k}{\sum \sum }}p_{jk}^{2}}}} Here
Kaiser–Meyer–Olkin_test
Indian Army soldier
Every year a seat is left empty for the journey to his hometown and three soldiers accompany the Baba to his home. A small sum of money is contributed by
Baba_Harbhajan_Singh
English footballer (born 1975)
the media effect, in the press release they decided to list the potential sum that Beckham could make over the five-year period from all his revenue sources
David_Beckham
Theorem in fluid mechanics
The total time T {\displaystyle T} taken to drain all the water and hence empty the vessel is found by setting h ( T ) = 0 {\displaystyle h(T)=0} and re-arranging:
Torricelli's_law
American TV series
featuring home buyers who have won lotteries or suddenly inherited a large sum of money. It is hosted by David Bromstad. It premiered on March 7, 2015.
My_Lottery_Dream_Home
American astronaut (1930–2012)
his permission. The lawsuit was settled out of court for an undisclosed sum, which Armstrong donated to Purdue. For many years, he wrote letters congratulating
Neil_Armstrong
2007 film by Ethan and Joel Coen
Moss (Brolin), a Vietnam War veteran and welder who stumbles upon a large sum of money in the desert, Anton Chigurh (Bardem), a hitman who is sent to recover
No_Country_for_Old_Men
President of Iraq from 1979 to 2003
exchange reserves, and state-controlled enterprises and diverted significant sums of Iraqi state funds through opaque financial networks under his authority
Saddam_Hussein
EMPTY SUM
EMPTY SUM
Boy/Male
American, Australian, Danish, French, Jamaican, Latin
Vain; Empty; Poor; Robbed; Hollow
Surname or Lastname
English
English : nickname for a foolish or eccentric person, from a diminutive of Foll, from Old French fol ‘mad’, ‘stupid’ (Late Latin follis, originally a noun denoting any of various objects filled with air, but later transferred to vain and empty-headed notions).
Girl/Female
Biblical
Empty, temple of the head.
Biblical
den; cave; making empty
Boy/Male
Biblical
Who is empty or exhausted.
Boy/Male
Arabic
Empty.
Girl/Female
Biblical
Den, cave, making empty.
Biblical
who is empty, exhausted;free, empty, exhausted;
Boy/Male
Hindu
One who is empty, Hollow, Vain
Surname or Lastname
English
English : occupational name for a carrier, from Middle English sum(p)ter ‘(driver of a) pack animal’.
Boy/Male
Tamil
One who is empty, Hollow, Vain
Boy/Male
British, English, Spanish
Strong Leader; Empty
Girl/Female
Biblical
Void, empty.
Boy/Male
Hindu, Indian
Empty
Biblical
empty; temple of the head
Girl/Female
Muslim
Fruit, Summer fruit
Surname or Lastname
English
English : variant of Sumpter.Fort Sumter, SC, was named in honor of Thomas Sumter, known as the ‘Gamecock of the Revolution’ for the fear he inspired in the British and Tory forces and the pivotal role he played in key American victories. Born in 1734 near Charlottesville, VA, he was of Welsh heritage; his ancestors probably emigrated to America in the late 17th century.
Biblical
den; making empty; watching
Girl/Female
Biblical
Den, making empty, watching.
Boy/Male
Arabic, Australian, German, Greek, Kurdish
Empty; Void
EMPTY SUM
EMPTY SUM
Biblical
ark; song; joyful cry
Girl/Female
Tamil
Akshika | அகà¯à®·à¯€à®•à®¾
One with good eyes
Boy/Male
Hindu, Indian
: Beauty of Lord Krishna
Surname or Lastname
English
English : habitational name from Gledhill, a place in West Yorkshire, named from Old English gleoda ‘kite’ + hyll ‘hill’.
Male
Norse
Old Norse name composed of the elements sumar "summer" and liði "one who fares," hence "summer traveler."
Boy/Male
Assamese, Hindu, Indian, Kannada, Sindhi, Tamil, Telugu
Lord Murugan
Female
English
Variant spelling of English Belle, BELL means "beautiful."Â
Female
Finnish
Finnish myth name of a sprite, possibly TERHENETÄR means "acorn."
Girl/Female
Muslim
Gorgeous
Girl/Female
Buddhist, Indian
A Goddess
EMPTY SUM
EMPTY SUM
EMPTY SUM
EMPTY SUM
EMPTY SUM
v. t.
To empty.
a.
Empty.
v. t.
To empty.
v. t.
To empty.
a.
To empty.
p. pr. & vb. n.
of Empty
pl.
of Empty
v. i.
To become empty.
a.
Empty; frivolous.
n.
An empty box, crate, cask, etc.; -- used in commerce, esp. in transportation of freight; as, "special rates for empties."
superl.
Destitute of, or lacking, sense, knowledge, or courtesy; as, empty brains; an empty coxcomb.
superl.
Destitute of effect, sincerity, or sense; -- said of language; as, empty words, or threats.
superl.
Destitute of reality, or real existence; unsubstantial; as, empty dreams.
superl.
Containing nothing; not holding or having anything within; void of contents or appropriate contents; not filled; -- said of an inclosure, as a box, room, house, etc.; as, an empty chest, room, purse, or pitcher; an empty stomach; empty shackles.
imp. & p. p.
of Empty
v. t.
To deprive of the contents; to exhaust; to make void or destitute; to make vacant; to pour out; to discharge; as, to empty a vessel; to empty a well or a cistern.
compar.
of Empty.
superl.
Producing nothing; unfruitful; -- said of a plant or tree; as, an empty vine.
a.
Empty.
n.
Love of empty of empty talk or noise.