residue
Pluralresidues
- 1The part that is left behind once something else has been taken away or used up.
A sticky residue coated the jar long after the honey was gone.
Cleaning sprays often leave a faint residue on glass surfaces.
Similardeposit, remnant, trace, film
Note
Latin supplied the image: residuum, from resideō, "I remain behind," reached English through Old French residu. The same Latin word also entered English unchanged as residuum, a doublet that lives beside residue. In everyday use residue usually suggests a thin trace or film, often unwanted: a sticky residue, a soapy residue. It works both as a mass noun and as a countable one.
- 2Material left behind when a liquid is removed or a mixture is separated, for example by filtration, evaporation, or distillation.
After distillation, the chemist weighed the residue at the bottom of the flask.
Evaporating the seawater leaves a salty residue rich in minerals.
Similardeposit, sediment, residuum
Note
In the laboratory the word names what stays put while the rest leaves: the solid in the flask after distillation, the crust after evaporation, the material held back on the filter. It is often the thing a chemist weighs. The plural appears when separations are compared, as in residues from different samples. Unlike the everyday leftover, it implies a deliberate process rather than mere neglect.
- 3The property and effects left in an estate after all debts and charges are paid and specific bequests are deducted.
Under the will, the residue passes to the testator's surviving children.
The executor distributed the residue once every creditor had been settled.
Similarremainder, residuum, balance
Note
The share of an estate settled last, because its size is known only once everything else has been paid. It passes under the will's residuary clause, and in drafting the adjective residuary is the usual companion form, as in the residuary estate. A gift of the residue stands in contrast to a specific bequest of a named item.
- 4A molecule, such as an amino acid in a polypeptide chain, released from a polymer when the bonds between neighboring monomers are broken.
The enzyme cleaves the polypeptide, freeing one amino acid residue at a time.
Each residue in the chain contributes to the protein's final folded shape.
Note
Biochemists use the word for a monomer treated as a unit of the chain, whether it is still bonded in place or freed by cleavage. It turns up most often in amino acid residue, and it lets a protein's length be stated as a count of residues. Where the laboratory leftover is usually a mass of material, here the word normally names a single unit you can count.
- 5The nonnegative remainder left after dividing a number by a base; a representative of an equivalence class modulo that base, usually taken between zero and the base.
Working modulo 7, the number 23 has a residue of 2.
Each integer reduces to a unique residue in the range zero to four when working modulo five.
Similarremainder
Note
Number theory's word for a remainder, with a subtlety. Strictly, the residue stands for a whole class of congruent integers, and the convention of choosing from [0, n) picks one tidy representative. That is why 23 and 2 count as the same residue modulo 7. The word almost always travels with its base: a residue modulo 7, or a residue mod 7 in speech.
- 6A complex number associated with a singularity of a meromorphic function, proportional to the contour integral of the function along a path enclosing that point.
She computed the residue of the function at its simple pole.
Summing each residue inside the loop gives the value of the contour integral.
Note
Complex analysts read it off a Laurent expansion: it is the coefficient of the (z − z₀)⁻¹ term, the one piece that survives integration around the singularity. Hence the verbs that go with it: one computes or takes residues, as in "by taking residues" in the Publications of the Research Institute for Mathematical Sciences (2001). Its kinship with the remainder after division lies only in the shared image of something left over.
Practice
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Origin
This word came through Middle English and Old French residu from Latin residuum, the neuter of residuus ("remaining"), which derives from resideō ("I remain behind"). It is a doublet of residuum.