Abundant number

Abundant number
Number Num"ber (n[u^]m"b[~e]r), n. [OE. nombre, F. nombre, L. numerus; akin to Gr. no`mos that which is dealt out, fr. ne`mein to deal out, distribute. See {Numb}, {Nomad}, and cf. {Numerate}, {Numero}, {Numerous}.] 1. That which admits of being counted or reckoned; a unit, or an aggregate of units; a numerable aggregate or collection of individuals; an assemblage made up of distinct things expressible by figures. [1913 Webster]

2. A collection of many individuals; a numerous assemblage; a multitude; many. [1913 Webster]

Ladies are always of great use to the party they espouse, and never fail to win over numbers. --Addison. [1913 Webster]

3. A numeral; a word or character denoting a number; as, to put a number on a door. [1913 Webster]

4. Numerousness; multitude. [1913 Webster]

Number itself importeth not much in armies where the people are of weak courage. --Bacon. [1913 Webster]

5. The state or quality of being numerable or countable. [1913 Webster]

Of whom came nations, tribes, people, and kindreds out of number. --2 Esdras iii. 7. [1913 Webster]

6. Quantity, regarded as made up of an aggregate of separate things. [1913 Webster]

7. That which is regulated by count; poetic measure, as divisions of time or number of syllables; hence, poetry, verse; -- chiefly used in the plural. [1913 Webster]

I lisped in numbers, for the numbers came. --Pope. [1913 Webster]

8. (Gram.) The distinction of objects, as one, or more than one (in some languages, as one, or two, or more than two), expressed (usually) by a difference in the form of a word; thus, the singular number and the plural number are the names of the forms of a word indicating the objects denoted or referred to by the word as one, or as more than one. [1913 Webster]

9. (Math.) The measure of the relation between quantities or things of the same kind; that abstract species of quantity which is capable of being expressed by figures; numerical value. [1913 Webster]

{Abstract number}, {Abundant number}, {Cardinal number}, etc. See under {Abstract}, {Abundant}, etc.

{In numbers}, in numbered parts; as, a book published in numbers. [1913 Webster]


The Collaborative International Dictionary of English. 2000.

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  • Abundant number — Abundant A*bun dant, a. [OE. (h)abundant, aboundant, F. abondant, fr. L. abudans, p. pr. of abundare. See {Abound}.] Fully sufficient; plentiful; in copious supply; followed by in, rarely by with. Abundant in goodness and truth. Exod. xxxiv. 6.… …   The Collaborative International Dictionary of English

  • Abundant number — In mathematics, an abundant number or excessive number is a number n for which σ ( n ) > 2 n . Here σ ( n ) is the sum of divisors function: the sum of all positive divisors of n , including n itself. The value σ ( n ) − 2 n is called the… …   Wikipedia

  • abundant number — noun : an imperfect number that is less than the sum of all its divisors (as 12) * * * Math. a positive number that is less than the sum of all positive integers that are submultiples of it, as 12, which is less than the sum of 1, 2, 3, 4, and 6 …   Useful english dictionary

  • abundant number — Imperfect Im*per fect, a. [L. imperfectus: pref. im not + perfectus perfect: cf. F imparfait, whence OE. imparfit. See {Perfect}.] 1. Not perfect; not complete in all its parts; wanting a part; deective; deficient. [1913 Webster] Something he… …   The Collaborative International Dictionary of English

  • abundant number — noun A number that is less than the sum of all of its divisors except itself. The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30, and 1 + 2 + 3 + 5 + 6 + 10 + 15 = 42, which is greater than 30, so 30 is an abundant number. Syn: excessive number …   Wiktionary

  • abundant number — Math. a positive number that is less than the sum of all positive integers that are submultiples of it, as 12, which is less than the sum of 1, 2, 3, 4, and 6. Cf. deficient number, perfect number. * * * …   Universalium

  • Colossally abundant number — In mathematics, a colossally abundant number (sometimes abbreviated as CA) is a natural number that, in some rigorous sense, has a lot of divisors. Formally, a number n is colossally abundant if and only if there is an ε > 0 such… …   Wikipedia

  • Highly abundant number — In mathematics, a highly abundant number is a natural number where the sum of its divisors (including itself) is greater than the sum of the divisors of any natural number less than it.Highly abundant numbers and several similar classes of… …   Wikipedia

  • Abundant — A*bun dant, a. [OE. (h)abundant, aboundant, F. abondant, fr. L. abudans, p. pr. of abundare. See {Abound}.] Fully sufficient; plentiful; in copious supply; followed by in, rarely by with. Abundant in goodness and truth. Exod. xxxiv. 6. [1913… …   The Collaborative International Dictionary of English

  • Number — Num ber (n[u^]m b[ e]r), n. [OE. nombre, F. nombre, L. numerus; akin to Gr. no mos that which is dealt out, fr. ne mein to deal out, distribute. See {Numb}, {Nomad}, and cf. {Numerate}, {Numero}, {Numerous}.] 1. That which admits of being counted …   The Collaborative International Dictionary of English

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