22C:096
Computation, Information, and Description

Department of Computer Science
The University of Iowa

Lecture Notes

Lecture 1

Definition of "discrete"

To be confused with "discreet."

From Webster's New World Dictionary.

discrete
1. separate and distinct. 2. made up of distinct parts.

From the Oxford English Dictionary.

discrete (dI'skri:t), a. (sb.) Also 6 discreet.
`separate, distinct', pa. pple. of discern re to separate, divide, DISCERN: cf. later sense of Fr. discret, discrete `divided, separate'. In the sense of cl. L. discretus, discrete was used by Trevisa (translating from L.), but app. was not in general use till late in 16th c. But in another sense, `discerning, prudent' (derived through French), discret, discrete was well-known in popular use from the 14th c.; this, even in late ME., was occasionally spelt discreet, which spelling was appropriated to it about the time that discrete in the L. sense began to be common; so that thenceforth discrete and discreet were differentiated in spelling as well as in meaning: see DISCREET. Before this, while discrete was the prevalent form for the later discreet, it is only rarely (see 1 B below) that discreet appears for the present discrete.
A adj.
1 a Separate, detached from others, individually distinct. Opposed to continuous. 1398 TREVISA Barth. De P.R. XIX. cxvi. (1495) 919 One is the begynnynge of alle thynges that is contynual and dyscrete. 1570 DEE Math. Pref. 13 Of distinct and discrete Vnits. 1594 BLUNDEVIL Exerc. III. I. xxxi. (ed. 7) 339 Of which Arkes some are called continuall, and some discrete or divided. 1594 BLUNDEVIL Exerc., III. I. xxxi. (ed. 7) 339 That Arke is called discrete or broken, which doth not take his beginning from the first point of Aries. 1634 PEACHAM Gentl. Exerc. III. 137 Raine or water..being divided by the cold ayre, in the falling downe, into discreet parts. 1775 HARRIS Philos. Arrangem. (1841) 308 The motion of all animals..by being alternate, is of the discrete kind. 1851 NICHOL Archit. Heav. 47 Any telescope capable of resolving these various masses into discrete stars. 1883 A. BARRATT Phys. Metempiric 59 To hold together, and keep discrete, simultaneous phenomena. Bspelt discreet. 1590 SPENSER F.Q. II. xii. 71 The waters fall with difference discreet, Now soft, now loud, unto the wind did call.
b Music. Applied to tones separated by fixed or obvious steps or intervals of pitch, as the notes of a piano; also to a movement of the voice from one pitch to another, as distinguished from a concrete movement or slide. Cf. CONCRETE 1 b. 1864 WEBSTER cites RUSH.
c Pathol. Separate, not coalescent or confluent: applied to stains, spots, or pustules, when scattered separately from each other over a surface, as in discrete small-pox F. variole discrete. 1854-67 C. A. HARRIS Dict. Med. Terminol. 218. 1882 CARPENTER in 19th Cent. Apr. 531 The discrete, `distinct', or `benign' form being by no means a severe disease, even among the unvaccinated. 1893 Daily News 4 Mar. 5/4 A woman..whose children had been removed for discrete smallpox.
d Logic. Individually distinct, but not different in kind. 1837-8 SIR W. HAMILTON Logic xi. (1866) I. 209 In so far as Conspecies are considered to be different but not contradictory, they are properly called Discrete or Disjunct Notions. 1837-8 SIR W. HAMILTON Logic xii.(1860) I. 224 Notions co-ordinated in the quantity or whole of extension..are only relatively different (or diverse); and in logical language are properly called Disjunct or Discrete Notions. 1864 BOWEN Logic iv. 66.
e discrete degrees: applied by Swedenborg to the various degrees or levels of spiritual existence, conceived as so distinct and separate from each other, as to render it impossible for any subject to pass out of that one for which he is constituted. 1788 tr. Swedenborg's Wisd. Angels III. f236 In every Man from his Birth there are three Degrees of Altitude, or discrete Degrees, one above or within another. 1856 GRINDON Life (1863) 319 Where things are differentiated by a discrete degree, the commencement of the new one is..on a distinct and higher level.
2 a Consisting of distinct or individual parts; discontinuous. discrete quantity, quantity composed of distinct units, as the rational numbers; number. Distinguished from continuous quantity = magnitude. 1570 BILLINGSLEY Euclid II. i. 62 Two contrary kynds of quantity, quantity discrete or number, and quantity continual or magnitude. 1687 H. MORE Answ. Psychop. (1689) 123 Inseperability, continued Amplitude, belongs to Spirits as well as discrete Quantity. 1785 REID Int. Powers III. iii. 311 Duration and extension are not discrete, but continued quantity. 1785 REID Int. Powers 342 Number is called discrete quantity, because it is compounded of units. 1837-9 HALLAM Hist. Lit. II. viii. II. 322 note, They were dealing with continuous or geometrical, not merely with descrete or arithmetical quantity. 1876 H. SPENCER Princ. Sociol. (1877) I. 475 The parts of an animal form a concrete whole; but the parts of a society form a whole that is discrete. 1893 FORSYTH Th. Functions 584 If there be no infinitesimal substitution, then the group is said to be discontinuous, or discrete. 1893 HARKNESS & MORLEY Th. Functions 50 To Hankel we owe the idea of a discrete mass of points.
b Belonging to, pertaining to, or dealing with, distinct or disconnected parts. discrete proportion = DISCONTINUED proportion. 1660 R. COKE Justice Vind. 23 All Geometrical proportion is either discrete, or continued. Discrete is, when the similitudo rationum is only between the 1. and the 2. and the 3. and 4. term. 1706 PHILLIPS (ed. Kersey), Discrete or Disjunct Proportion. 1856 DOVE Logic Chr. Faith 422 note, Scepticism is discrete and proceeds in detail.
3 Gram. & Logic. Of conjunctions: adversative. Of propositions: discretive. Applied also to the two members of such a proposition, separated by the adversative conjunction. Obs. 1628 T. SPENCER Logick 237 That Axiome is discrete, that hath a discrete Coniunction for the band thereof. 1628 T. SPENCER Logick 239 The coniunction which tyes the parts together, is called discrete: and in this place it imports no more but a thing that keepes two asunder, for the present. A. 1638 MEDE Apost. latter Times i. Wks. 1672 III. 623 The Words..of my Text [Nevertheless, the Spirit, etc. 1 Tim. iv. 1] depend upon the last of the former Chapter, as the second part of a Discrete proposition. 1654 Z. COKE Logick (1657) 119 A discrete sentence, is, which hath a discrete conjunction; as, although, yet, notwithstanding, etc. 1664 H. MORE Myst. Iniq. Apol. 538 [It will] run in this form of a Discrete Axiome, I will have you wait on me at such a meeting, though your cloaths be old or out of the mode.
4 Metaph. Not concrete; detached from the material, abstract. 1854 Fraser's Mag. L. 343 The mental march from concrete or real notions to discrete or abstract truths. 1862 H. SPENCER First Princ. (1870) 27 This formation of symbolic Conceptions, which inevitably arises as we pass from small and concrete objects, to large and to discrete ones.
B sb. A separate part. 1890 J. H. STIRLING Gifford Lect. xviii. 353 Break it up into an end- less number of points..an endless number of discretes.1967 Electronics 6 Mar. 116 Integrated circuits will be turning up routinely in new products throughout 1967. The big switch from discretes is on.
discrete,
early form of DISCREET.
di'screte, v. Obs. stem of discern re to separate: see DISCERN.] trans.
To divide into discrete or distinct parts; to separate distinctly, dissever. 1646 SIR T. BROWNE Pseud. Ep. II. i. 55 The reason thereof is its continuity, as..its body is left imporous and not discreted by atomicall terminations. 1656 BLOUNT Glossogr., Discreted, severed, parted, discerned. 1857-8 SEARS Athan. vii. 316 This essential dualism discretes for ever the two worlds of spirit and matter.

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