Title: 03. Vokabular

Q: [001] ab
A: off, away, down

Q: [002] abändern
A: (ab + ander + (n))
to alter, to modify, to vary

Q: [003] aber
A: but, however

Q: [004] abgeändert
A: (p.p. of: abändern)
modified, altered, varied

Q: [005] abgekürtz
A: (p.p. of: abkürzen)
abbreviated, shortened

Q: [006] Abkürzung
A: (ab + kurz + ung)
abbreviation

Q: [007] absolut
A: absolute

Q: [008] Addition
A: addition

Q: [009] ähnlich
A: similar, analogous to, resembling

Q: [010] alle
A: all

Q: [011] Allgemeinheit
A: generality, universality

Q: [012] als
A: as, like, when, than

Q: [013] alsdann
A: then

Q: [014] also
A: so that, then, therefore

Q: [015] alt
A: old

Q: [016] an
A: at, by, along, against, to, in, on, in respect to. (N.B. an-, vor-, etc. may split off from the verbs of which they are prefixes and appear separately later in the sentence.)

Q: [017] an- (prefix)
A: at, toward, commence to, continue to

Q: [018] Analoga
A: (Greek) analogues

Q: [019] Analysis
A: analysis

Q: [020] ander
A: other, another (cog., other)

Q: [021] andernfalls
A: (ander + (n) + falls)
otherwise, else

Q: [022] anderseits
A: (ander + seits)
on the other hand, on the other side

Q: [023] Anfang
A: beginning, start, origin

Q: [024] angehören
A: to belong (to), to pertain (to), to be related (to)

Q: [025] angehörig
A: belonging, related

Q: [026] angewendet
A: (p.p of: anwenden)
applied, employed, used

Q: [027] annehmen
A: (an + nehmen)
to assume, to suppose, to undertake, to take, to accept

Q: [028] anwenden
A: (an + wenden)
to apply, to use, to employ (a thing)

Q: [029] Äquivalenzzeichen
A: (Äquivalenz + Zeichen)
equivalence sign

Q: [030] Art
A: kind, sort, manner

Q: [031] assoziativ
A: associative

Q: [032] auch
A: also; too, even
-- nicht, neither

Q: [033] auf
A: on, upon, in, at; into, to; up, upward

Q: [034] aufgeschreiben
A: (p.p. of: aufscheiben)
written down

Q: [036] aufzählen
A: (auf + zählen)
to enumerate, to count, to list

Q: [037] aufzuzählen
A: See: aufzählen

Q: [038] aus
A: out of, from, away from (cog., out)

Q: [039] aus- (prefix)
A: out, forth; thoroughly, sufficiently

Q: [040] Ausdruck
A: (aus + Druck)
expression

Q: [035] aufschreiben
A: (auf + schreiben)
to write down

Q: [041] ausführlich
A: full, complete, detailed

Q: [042] ausführlicher
A: (comparative of adverb: ausführlich)
more fully, more completely

Q: [043] Ausnahme
A: exception

Q: [044] ausnahmsweise
A: (from: Ausnahme + Weise)
by way of exception

Q: [045] ausschliessen
A: (aus + schliessen)
to exclude

Q: [046] Axiom(e)
A: axiom(s)

Q: [047] be- (prefix)
A: Roughly corresponds to be- and en-, as in besprinkle, bewitch, enrich, enslave.

Q: [048] beachten
A: to notice, to consider, to observe

Q: [049] bedeuten
A: to mean, to signify

Q: [050] Bedingung
A: condition

Q: [051] befürchten
A: to fear

Q: [052] Begriff
A: (be + Griff)
concept, idea

Q: [053] Behauptung
A: (be + Haupt + ung)
proposition, assertion

Q: [054] bei
A: at, by, among, near, with, about

Q: [055] beide
A: both (cog., both)

Q: [056] beim
A: abbr. of: bei dem

Q: [057] Beispiel
A: example; zum --, for example

Q: [058] bekannt
A: known

Q: [059] beliebig
A: (from: belieben, to be pleased with; lieben, to love)
arbitrary

Q: [060] Bemerkung
A: (be + merk(en) + ung)
observation, remark, notice

Q: [061] benutzen
A: to use, to employ, to utilize

Q: [062] benutzt
A: (from: benutzen, to use)
used, utilized

Q: [063] benutzten
A: See: benutzt

Q: [064] Benützung
A: use, utilization

Q: [065] besagen
A: (be + sagen)
to mean, to signify

Q: [066] beschaffen
A: (be + schaffen)
constituted; to procure, to supply, to get

Q: [067] Beschränkung
A: limitation, restriction

Q: [068] bestehen
A: to pass through, to meet with; to exist, to subsist; -- aus, to consist of; -- in, to consist in; Bestehen, existence, validity (of an equation)

Q: [069] bestimmt
A: determined; precise(ly), exact(ly); fixed

Q: [070] betrachten
A: to consider, to regard, to view

Q: [071] Betrag
A: amount, sum; absoluter --, absolute value

Q: [072] betreffen
A: to concern, to have to do with, to affect

Q: [073] betrifft
A: (3 sing. pres. of: betreffen)
concerns, has to do with, affects

Q: [074] Beweis
A: proof

Q: [075] beweisen
A: to prove, to demonstrate

Q: [076] bewiesen
A: (p.p. of: beweisen)
proved, proven

Q: [077] bezeichnen
A: to designate, to denote, to indicate (cog., to betoken)

Q: [078] bezeichnet
A: (p.p. of: bezeichnen)
designated, denoted, indicated

Q: [079] beziehen
A: to relate, refer

Q: [080] Beziehung
A: relation, correspondence

Q: [081] bezogen
A: (p.p. of: beziehen)
related, referred

Q: [082] Bezug
A: relation, reference; in--auf, in reference to, with regard to

Q: [083] bilden
A: to form, to establish

Q: [084] bis
A: up to, as far as, until; except

Q: [085] bisher
A: (bis + her)
hitherto, till now, as far as here

Q: [086] bleiben
A: to remain, to stay, to last (cog. (be)leave)

Q: [087] brauchen
A: to need, to use (cog., to brook)

Q: [088] Bruch (pl.: Brüche)
A: (from: brechen, to break) fraction

Q: [089] Buch
A: book

Q: [090] Buchstabe
A: (from: Buch + Stab)
letter

Q: [091] Buchstabenvertauschung
A: (Buchstaben + Vertauschung)
interchange of letters

Q: [092] bzw.
A: abbr. (= beziehungsweise)
respectively, or; a bzw. b, a and b respectively

Q: [093] da
A: (adverb) there, present, here;
(conjunction) as, when, while, since

Q: [094] dabei
A: (da + bei)
therewith, thereby, by it, with it, moreover, in view of it (etc.)

Q: [095] daher
A: (da + her)
hence, therefore

Q: [096] danach
A: after that, thereupon, subsequently; according to, accordingly

Q: [097] dann
A: then; -- und nur --, if and only if

Q: [098] darf
A: (1. & 3. sing. pres. of dürfen)
may

Q: [099] dargestellt
A: (p.p. of: darstellen)
represented, produced, displayed

Q: [100] darstellen
A: to represent, to produce, to display

Q: [101] Darstellung
A: representation, presentation

Q: [102] das
A: See: der, die, das

Q: [103] dass
A: (conjunction) that

Q: [104] dasselbe
A: See: derselbe

Q: [105] dazu
A: (da + zu)
in addition, for that purpose, thereto, besides

Q: [106] decken
A: to cover; --sich, to coincide (with), to be identical (cog., deck)

Q: [107] Dedekind
A: Richard Dedekind (1831 - 1916)

Q: [108] Dedekindscher
A: (adj.) Dedekind

Q: [109] definieren
A: to define

Q: [110] Definition
A: definition

Q: [111] dem, den
A: See: der, die, das

Q: [112] demnach
A: (dem + nach)
accordingly

Q: [113] denselben
A: See: derselbe

Q: [114] der, die, das, des, dem, den, deren, denen
A: (article) the, of the, to the;
(rel. pronoun) who, whose, to whom, which, of which (etc.);
(cog., there)

Q: [115] derart
A: (der + Art)
in such a way, so much

Q: [116] derartig
A: of that kind, such

Q: [117] deren
A: (rel. pronoun) Genitive plural of der, die, das

Q: [118] derjenige, diejenige, dasjenige
A: he who, she who, that which; the, those

Q: [119] derselbe, dieselbe, dasselbe
A: (der + selb + (e))
the same

Q: [120] des
A: (article) of the;
(pronoun) whose, of which

Q: [121] deutsch
A: (adjective) German

Q: [122] d.h.
A: abbr. (= das heißt)
that is, i.e.

Q: [123] dies
A: this. -selbe. See: derselbe

Q: [124] Differenz
A: difference

Q: [125] Ding
A: thing, object

Q: [126] distributiv
A: distributive

Q: [127] drei
A: three

Q: [128] dritte
A: third

Q: [129] Druck
A: pressure, impression, print

Q: [130] durch
A: through; by, owing to (cog., thorough, through (cf. thoroughfare, through way)).

Q: [131] durchweg
A: (durch + weg)
throughout, ordinarily

Q: [132] eben
A: even, just, level; evenly, exactly

Q: [133] ebenso
A: (eben + so)
likewise, just so, just as

Q: [134] Eigen
A: own, proper (cog., own)

Q: [135] Eigenschaft
A: (Eigen + schaft)
property, quality, characteristic

Q: [136] ein
A: (indef. article) a, an;
(numeral) one

Q: [137] ein-
A: (prefix)
1. one-, uni-;
2. in-

Q: [138] eindeutig
A: having but one meaning, unambiguous, one-valued, well-defined; --e Zuordnung, one-valued correspondence

Q: [139] ein-eindeutig
A: one-to-one

Q: [140] einfach
A: simple, simply, single, elementary

Q: [141] eingeklammert
A: enclosed in parentheses

Q: [142] einige
A: several, some

Q: [143] einiges
A: something

Q: [144] Einklang
A: (ein + Klang)
agreement, accord, harmony

Q: [145] einmal
A: (ein + Mal)
once, ever;
nitch --, not even

Q: [146] Einordnung
A: (ein + Ordnung)
ordering, arrangement

Q: [147] Einselement
A: unit element

Q: [148] einstweilen
A: in the meantime, for the present

Q: [149] einteilig
A: (ein + Teil + ig)
made of one part, single

Q: [150] Einteilung
A: (ein + Teil + lung)
division, separation, classification

Q: [151] einwandfrei
A: (Einwand, objection + frei),
unobjectionable

Q: [152] ent-
A: Prefix usually denoting negation, deprivation, or separation; or  starting of an action

Q: [153] enthalt
A: (3. sing. pres. of: enthalten)
contains, includes

Q: [154] enthalten
A: to contain, to include

Q: [155] entsprechen
A: (ent + sprechen)
to correspond

Q: [156] entsprechend
A: corresponding(ly)

Q: [157] entstehen
A: (ent + stehen)
to originate (from), to be formed (by)

Q: [158] entstehend
A: (pres. p. of: entstehen)
originating (from), formed (by)

Q: [159] entweder
A: either

Q: [160] Entwicklung
A: development

Q: [161] er-
A: Prefix often denoting start or completion of action; with adjectives, the act of becoming

Q: [162] erfüllen
A: (er + füllen)
to fill up, to fulfill, to satisfy

Q: [163] Ergänzung
A: (from: ganz)
completion, supplement

Q: [164] ergeben
A: (er + geben) to yield

Q: [165] erhalten
A: to obtain, to keep, to preserve, to get, to acquire; -- bleiben, to remain unchanged

Q: [166] erheben
A: (er + heben)
to raise, to rise, to lift

Q: [167] erklären
A: (er + klären)
to explain, to explicate, to announce

Q: [168] erledigen
A: to accomplish, to dispose of, to settle, to bring to a close

Q: [169] erschaffen
A: (er + schaffen) to create

Q: [170] erschöpfen
A: to exhaust

Q: [171] ersetzen
A: (er + setzen) to replace, to substitute

Q: [172] erst
A: first; --ere, the former

Q: [173] erzeugen
A: to form, to produce, to generate; -- sich, to form

Q: [174] es
A: (pron.) it; -- gibt, there is, there are (cog., it)

Q: [175] etwaig
A: possible

Q: [176] Existenz
A: existence

Q: [177] existieren
A: to exist

Q: [178] Fall
A: case, event (cog. fall, befall)

Q: [179] Fälle
A: (plural of: Fall) cases, events

Q: [180] falls
A: in case, if

Q: [181] Fallunterscheidung
A: (Fall + Unterscheidung) distinction of cases

Q: [182] fassen
A: to seize, to hold, to form (an idea, etc.);
to comprise

Q: [183] fern
A: far

Q: [184] ferner
A: (comparative of: fern)
further; moreover, also

Q: [185] fest
A: fixed, permanent;
a sei --, let a be held constant;
(cog., fast)

Q: [186] feststehen
A: (fest + stehen)
to be established, to be settled, to be stationary

Q: [187] fliessend
A: flowing, ensuing

Q: [188] flüssig
A: fluid

Q: [189] Folge
A: sequence, sucession; consequence, result; conclusion, inference

Q: [190] folgen
A: to follow (cog., follow)

Q: [191] folgendermassen
A: as follows

Q: [192] folgern
A: to conclude, to infer

Q: [193] folglich
A: consequently

Q: [194] folgt
A: (3. sing. pres. of: folgen) follows;
aus a -- b, if a then b

Q: [195] fordern
A: to demand, to request

Q: [196] Forderung
A: requirement

Q: [197] Formel
A: formula

Q: [198] formulieren
A: to formulate

Q: [199] Formulierung
A: formulation

Q: [200] fort
A: forth, forward, on; away, gone

Q: [201] fortan
A: (fort + an) henceforth

Q: [202] frei
A: free

Q: [203] freigeworden
A: (frei + geworden)
freed, set free

Q: [204] führen
A: to lead; to carry, to bring

Q: [205] füllen
A: to fill

Q: [206] fünf
A: five

Q: [207] fünfte
A: fifth

Q: [208] für
A: for

Q: [209] ganz
A: whole, entire; --e Zahl, whole number

Q: [210] gar
A: entirely, quite

Q: [211] ge-
A: prefix forming past participles of verbs

Q: [212] geben
A: to give (cog., give)

Q: [213] gefolgert
A: See: folgern

Q: [214] gefordert
A: See: fordern

Q: [215] gegeben
A: (p.p. of: geben) given

Q: [216] gegen
A: against

Q: [217] gehen
A: to go;
geht nicht, cannot be done, is impossible (literally: goes not)

Q: [218] gehören
A: to belong

Q: [219] gehörig
A: belonging

Q: [220] gekehrt
A: (p.p. of: kehren) turned

Q: [221] gelten
A: to be valid, to apply, to be worth (cog., yield)

Q: [222] gemeint
A: (p.p. of: meinen)
meant, intended

Q: [223] genannt
A: (p.p. of: nennen) called

Q: [224] genau
A: exactly

Q: [225] genommen
A: (p.p. of: nehmen) taken

Q: [226] genug
A: enough (cog., enough)

Q: [227] genügen
A: (from: genug) to suffice, to satisfy

Q: [228] gerade
A: straight, just, exactly; even (number)

Q: [229] geradezu
A: (gerade + zu)
immediately, straightway

Q: [230] gerechtfertigt
A: justified

Q: [231] gesagt
A: (p.p. of sagen) said

Q: [232] Gesamtheit
A: totality, whole

Q: [233] Gesetz
A: law, rule

Q: [234] gesetzt
A: (p.p. of: setzen)
set, put, placed; granted (that), provided (that)

Q: [235] gesondert
A: (p.p. of: sondern)
separate(ly)

Q: [236] gespalten
A: See: spalten

Q: [237] gestellt
A: (p.p. of: stellen) put

Q: [238] getan
A: (p.p. of tun) done, made, effected

Q: [239] gewiss
A: certain, fixed, sure

Q: [240] geworden
A: (p.p. of: werden) having become

Q: [241] Gewünschte
A: (from: wünschen, to wish)
desired result, thing wished for

Q: [242] gibt
A: (3. sing. pres. of: geben) gives;
es --, there is given, there is, there exists;
zu a gibt es ein b (mit...), given a, there exists a b (such that...)
(Cog., giveth)

Q: [243] gilt
A: (3. sing. pres. of: gelten)
is valid, is worth, holds (true).

Q: [244] gleich
A: equal: (a)like, (the) same;
instantly, at once (cog., like)

Q: [245] Gleichheit
A: (gleich + heit) equality

Q: [246] Gleichheitszeichen
A: (Gleichheits + Zeichen) equality sign

Q: [247] Gleichung
A: equation

Q: [248] griechisch
A: (adjective) Greek

Q: [249] Griff
A: grip, seizing (cog., grip)

Q: [250] gross
A: large, big, great;
--e Buchstaben, capital letters
(cog., gross, grocer, Gross (name))

Q: [251] grösser
A: (comparative of: gross)
larger, greater, bigger;
-- als, greater than

Q: [252] grösste
A: (superlative of: gross)
largest, greatest

Q: [253] Grund
A: ground, reason;
auf -- von, on the basis of

Q: [254] Grundlage
A: (Grund + Lage)
foundation, basis, rudiment

Q: [255] haben
A: to have

Q: [256] halten
A: to hold, to keep

Q: [257] handeln
A: to act, to deal, to proceed

Q: [258] hat
A: (3. sing. pres. of: haben) has (cog., hath)

Q: [259] Haupt
A: principal, chief, main; head

Q: [260] Hauptsatz
A: (Haupt + Satz) main theorem

Q: [261] heben
A: to lift (cog., heave)

Q: [262] heissen
A: to call, to be called, to mean

Q: [263] heisst
A: (3. sing. pres. of: heissen)
is called, means, calls

Q: [264] -heit
A: (suffix) -ness, -hood (cog., -hood)

Q: [265] her
A: here, hither, from; since, ago

Q: [266] hier
A: here; in this case

Q: [267] hierin
A: herein

Q: [268] hiernach
A: (hier + nach)
according to this, after this

Q: [269] hierzu
A: (hier + zu)
to this, hereto, moreover, to it, for it

Q: [270] hinreichend
A: (from: hin + reichen, to reach there, i.e., to reach as far as necessary) sufficient(ly)

Q: [271] hoch
A: high;
a hoch b, a to the b

Q: [272] höchstens
A: (from: hoch) at most, at best (cog., (at) highest)

Q: [273] identisch
A: identical

Q: [274] Identität
A: identity

Q: [275] -ig
A: (suffix) -y

Q: [276] im
A: (= in dem) in the

Q: [277] in
A: in

Q: [278] Individuen
A: individuals

Q: [279] Induktion
A: induction

Q: [280] Induktionsaxiom
A: (Induktions + Axiom) axiom of induction

Q: [281] Inhalt
A: content, volume

Q: [282] Inhaltsverzeichnis
A: (Inhalts + Verzeichnis) table of contents, index

Q: [283] insbesondere
A: especially, in particular

Q: [284] Integralrechnung
A: (Integral + Rechnung) integral calculus

Q: [285] irgend
A: any, at all, some

Q: [286] irrational
A: irrational

Q: [287] ist
A: (3. sing. pres. of: sein) is;
-- a gegeben, so, if a is given, then

Q: [288] ja
A: yes, indeed

Q: [289] je
A: always, ever;
--nach, according to

Q: [290] jedenfalls
A: in any case, at any rate

Q: [291] jeder, jedes (etc.)
A: each, every

Q: [292] jetzt
A: now

Q: [293] kam
A: (sing. imperf. indic. of: kommen) came, arrived, happened

Q: [294] kann
A: (1 & 3. sing. pres. indic. of: können) can, is able

Q: [295] kanonisch
A: canonical

Q: [296] Kapitel
A: chapter, section, topic

Q: [297] kein(e)
A: no, none

Q: [298] -keit
A: (same as -heit) -hood, -ness

Q: [299] Kenner
A: expert, professional

Q: [300] Klang
A: sound

Q: [301] klar
A: obvious, evident; clear

Q: [302] klären
A: to clarify, to clear up

Q: [303] Klasse
A: class

Q: [304] klein
A: small, little, (of letters) lower case
(cog., clean, Klein, Kline)

Q: [305] kleiner
A: smaller, lesser

Q: [306] kleinste
A: smallest, least

Q: [307] kommen
A: to come

Q: [308] kommutativ
A: commutative

Q: [309] komplex
A: complex

Q: [310] kompliziert
A: complicated

Q: [311] konjugiert
A: conjugated

Q: [312] können
A: can, may, to be able

Q: [313] konstruierte
A: constructed

Q: [314] Konstruktion
A: construction

Q: [315] kurz
A: short (cog., curt, curtail)

Q: [316] Kürzung
A: shortening; cancellation (of a common factor)

Q: [317] lag
A: (sing. imperf. indic. of: liegen)
lay, was situated

Q: [318] Lage
A: layer, condition, situation

Q: [319] lang
A: long, tall

Q: [320] lassen
A: to let, to leave, to allow, to cause (something to be done);
-- sich, admit of, are capable of

Q: [321] lässt
A: (3. sing. pres. of: lassen) lets

Q: [322] lateinisch
A: (adjective) Latin

Q: [323] laut
A: (adverb) in accordance with

Q: [324] lauter
A: mere, pure; nothing but

Q: [325] lediglich
A: only, merely, entirely

Q: [326] leer
A: empty

Q: [327] Lehrbuch
A: textbook

Q: [328] leisten
A: to do, to perform, to accomplish, to effect

Q: [329] lernen
A: to learn

Q: [330] lernend
A: (present participle of: lernen) learning

Q: [331] letzte
A: last, latest, lowest;
der (die, das) letztere, the latter

Q: [332] -lich
A: -ly (cog., -ly (-like))

Q: [333] liefern
A: to furnish

Q: [334] liegen
A: to lie, to be situated

Q: [335] links
A: left, on the left

Q: [336] logisch
A: logical

Q: [337] Lösung
A: (from: lösen, to solve, to loosen) solution

Q: [338] machen
A: to make, to do, to cause

Q: [339] Mal
A: time, instance; times

Q: [340] man
A: (indefinite pronoun) one, they, we, you, a person;
-- sagt, they say, it is said; (cog., man)

Q: [341] mehr
A: more

Q: [342] meinen
A: to mean, to intend

Q: [343] meist
A: (superlative of: mehr) most, for the most part, generally

Q: [344] Menge
A: set, aggregate (cog., many)

Q: [345] merken
A: to notice, to note (cog., mark)

Q: [346] mindestens
A: at least

Q: [347] minus
A: minus

Q: [348] miss-
A: mis-, dis-

Q: [349] Missverständnis
A: (miss + Verständnis) misunderstanding, misconception

Q: [350] mit
A: with

Q: [351] mitbeweisen
A: (mit + beweisen)
to prove therewith, to prove at the same time

Q: [352] mittelbar
A: indirect, mediate

Q: [353] mögen
A: to be able to, to be willing, to be possible (cog., may)

Q: [354] möglich
A: (from: mögen)
possible, potential, feasible

Q: [355] Möglichkeit
A: possibility

Q: [356] Multiplikation
A: multiplication

Q: [357] müsste
A: (1. & 3. sing. imperf. indic. & subj. of: müssen)
was to (be), ought to (be), would, should, had to

Q: [358] mutatis mutandis
A: (Latin) with appropriate changes

Q: [359] nach
A: after, behind; to, toward; according to; by; at; in

Q: [360] nachdem
A: (nach + dem) according to the way that, according as; afterwards, after, when

Q: [361] Nachfolger
A: (nach + Folger) successor

Q: [362] nachgewiesen
A: proved, shown

Q: [363] nachher
A: (nach + her)
afterwards

Q: [364] nachst
A: next

Q: [365] Nachweis
A: demonstration, proof, indication, information

Q: [366] natürlich
A: of course; natural(ly);
--e Zahl, natural number

Q: [367] nebst
A: besides, in addition to

Q: [368] negativ
A: negative

Q: [369] nehmen
A: to take, to receive. (See: annehmen, zunehmen, etc., remembering that the prefix often appears further on in sentence.)

Q: [370] nennen
A: to name, to call, to mention (cog., name)

Q: [371] neu
A: new

Q: [372] neutral
A: neutral

Q: [373] nicht
A: not

Q: [374] nichts
A: nothing, none

Q: [375] Not
A: necessity (cog., need)

Q: [376] nötig
A: (from: Not) necessary

Q: [377] notwendig
A: (from: Not) necessary

Q: [378] Null
A: zero

Q: [379] nun
A: now

Q: [380] nunmehr
A: (nun + mehr) now, henceforth

Q: [381] nur
A: only, solely;
wenn --, provided only that

Q: [382] ober
A: upper; chief, high

Q: [383] Oberzahl
A: (ober + Zahl) number belonging to upper class, upper number (of a Dedekind cut)

Q: [384] obig
A: above-mentioned, above

Q: [385] oder
A: or

Q: [386] offen
A: open

Q: [387] offenbar
A: (from: offen) evident(ly), obvious(ly)

Q: [388] ohne
A: without

Q: [389] ordnen
A: to order (in the sense of arranging in order)

Q: [390] Ordnung
A: order, ordering

Q: [391] Paar
A: pair

Q: [392] paarweise
A: (Paar + Weise) in pairs

Q: [393] passend
A: appropriate, suitable

Q: [394] plus
A: plus

Q: [395] positiv
A: positive

Q: [396] Potenz
A: power

Q: [397] Produkt
A: product

Q: [398] promiscue
A: (Latin) interchangeably

Q: [399] Punkt
A: point; period, dot

Q: [400] rational
A: rational

Q: [401] rechnen
A: to compute, to reckon, to count

Q: [402] Rechnung
A: computation, counting, arithmetic, calculus

Q: [403] recht
A: right (in all its various senses); correct, right-hand, true

Q: [404] reell
A: real; --e Zahl, real number

Q: [405] Reihe
A: series; row, succession (cog., row)

Q: [406] Reihenfolge
A: (Reihen + Folge)
sequence, order, succession

Q: [407] rein
A: pure(ly)

Q: [408] Repräsentant
A: representative

Q: [409] Repräsentantenpaar
A: (Repräsentanten + Paar) pair of representatives

Q: [410] reservieren
A: to reserve

Q: [411] reserviert
A: reserved

Q: [412] resp.
A: abbr. (= respektiv) respectively;
a resp. b, a and b, respectively; a or b

Q: [413] Rücksicht
A: regard, consideration;
mit -- auf, with regard to, in consideration of

Q: [414] Rückwartslesen
A: (rückwarts + Lesen) reading backwards

Q: [415] ruhig
A: calm(ly), quiet(ly), smooth(ly), confident(ly)

Q: [416] sagen
A: to say, to tell, to speak (cog., say)

Q: [417] salopp
A: rough, sloppy

Q: [418] Satz
A: theorem, sentence, proposition

Q: [419] schaffen
A: to create (cog., shape)

Q: [420] -schaft
A: (cog., -ship)

Q: [421] schicken
A: to send;
-- sich, to happen, to be suitable (for)

Q: [422] schliessen
A: to close, to conclude; to draw a conclusion, to reason

Q: [423] Schnitt
A: cut

Q: [424] Schnitteigenschaft
A: (Schnitt + Eigenschaft) propert of a cut

Q: [425] schon
A: already; as yet, so far;
wenn --, ob --, though, although

Q: [426] schreibe
A: (sing. imperative of: schreiben) write, write as, written as

Q: [427] schreiben
A: to write (cog., scribe)

Q: [428] Schreibweise
A: (schreib + Weise) manner of writing, way of writing, notation

Q: [429] Schritt
A: step

Q: [430] sei
A: (pres. subjunctive & imperative sing. of: sein) let there be, let (be), may be, be;
sei a..., let a be...

Q: [431] Seite
A: side, page (of a book)

Q: [432] selbst
A: self, myself, yourself, himself, itself (etc.)

Q: [433] setzen
A: to assign a place to, to set

Q: [434] sich
A: (reflexive pronoun) itself, herself (etc.; often need not be translated)

Q: [435] sie
A: she, her, it, they

Q: [436] sind
A: (1. & 3. plur. pres. of: sein) are

Q: [437] Sinn
A: sense, meaning

Q: [438] so
A: so, thus, in such a manner;
ist (or sind)..., so..., if..., then...

Q: [439] soeben
A: (so + eben) just, just now

Q: [440] sogar
A: (so + gar) even

Q: [441] solch
A: such, such a

Q: [442] sollen
A: should, ought, to be obliged to, to be to, shall (cog., shall)

Q: [443] sondern
A: to sunder;
(conj.) but rather
(cog., sunder)

Q: [444] sonst
A: otherwise

Q: [445] sowohl
A: (so + wohl) as well;
-- a als auch b, both a and b

Q: [446] spalten
A: to split, to divide (in two), to separate

Q: [447] später
A: (comparative of: spät) later;
--hin, later on

Q: [448] speziell
A: special

Q: [449] Sprache
A: language (cog., speech)

Q: [450] sprechen
A: to speak, to say, to talk

Q: [451] sprich
A: (sing. imperative of: sprechen)
pronounced (as follows), read as

Q: [452] statt
A: instead of, in place of (cog., stead)

Q: [453] stehen
A: to stand, to be situated, to be;
stehen fest. See: feststehen
(cog., stay (stand))

Q: [454] Stelle
A: place, spot, position;
an -- von, in place of (cog., stall)

Q: [455] Stern
A: star, asterisk

Q: [456] stets
A: always

Q: [457] stimmen
A: to accord, to agree;
-- überein. See: übereinstimmen

Q: [458] Strich
A: line, bar, prime (cog., stroke)

Q: [459] Subtraktion
A: subtraction

Q: [460] Summand
A: summand, term of a sum

Q: [461] Summe
A: sum

Q: [462] symmetrisch
A: symmetrical

Q: [463] Tat
A: fact, deed, act;
in der --, in fact, indeed (cog., deed)

Q: [464] Teil
A: part, share, division (cog., deal)

Q: [465] Teilung
A: division, partition

Q: [466] Transitivität
A: transitivity

Q: [467] trivial(er)
A: trivial

Q: [468] trivialerweise
A: (trivialer + Weise) simply, trivially

Q: [469] tun
A: to do; to make, to effect (cog., do)

Q: [470] tut
A: (3. sing. pres. of: tun) does, makes, effects (cog., doeth)

Q: [471] über
A: over

Q: [472] überdies
A: (über + dies) besides, moreover

Q: [473] überdecken
A: (über + decken) to overlap, to cover with

Q: [474] übereinstimmen
A: (über + ein + stimmen) to coincide, to correspond, to agree

Q: [475] überflüssig
A: (über + flüss + ig) superfluous
(cog., over + flow + y)

Q: [476] übergehen
A: (über + gehen) to go over (into), to pass over, to turn (change) into

Q: [477] übersichtlich
A: (über + Sicht + lich) easy to survey, clearly arranged
(cogs., over + sight + like)

Q: [478] Übersichtlichkeit
A: lucidity, clearness

Q: [479] üblich
A: customary, usual

Q: [480] übrig
A: (from: über) remaining, left over, superfluous

Q: [481] u. dgl.
A: abbr. (= und dergleichen) etc., and the like

Q: [482] um
A: about, with regard to, in order to, to

Q: [483] umfassen
A: to embrace, to comprise

Q: [484] umgekehrt
A: conversely, inversely

Q: [485] umkehren
A: to turn back; to turn round, to reverse, to invert

Q: [486] un-
A: (prefix) un-

Q: [487] und
A: and

Q: [488] -ung
A: (suffix) -ing

Q: [489] ungleich
A: (un + gleich) unequal (cog., unlike)

Q: [490] unmittelbar
A: (un + mittelbar) immediate, direct

Q: [491] unnötig
A: (un + nötig) unnecessary

Q: [492] unser
A: our, ours, of us

Q: [493] unter
A: under, beneath, below, among;
unter A versteht man B, by A we mean [is meant] B;
(cog., under)

Q: [494] Unterfall
A: (unter + Fall) subordinate case

Q: [495] Unterklasse
A: (unter + Klasse) lower class (of a Dedekind cut)

Q: [496] unterscheiden
A: to distinguish, to differentiate

Q: [497] Unterscheidung
A: distinction, differentiation

Q: [498] Unterschied
A: difference

Q: [499] Unterzahl
A: lower number (of a Dedekind cut)

Q: [500] unverändert
A: (un+ver+ander+t) unchanged

Q: [501] unverträglich
A: inconsistent, incompatible

Q: [502] Unverträglichkeit
A: inconsistency, incompatibility

Q: [503] verbleiben
A: (from: bleiben) to remain

Q: [504] verlangen
A: to ask, to demand, to require; to desire, to long for

Q: [505] vermeiden
A: to avoid, to evade

Q: [506] vermieden
A: (p.p. of: vermeiden) avoided, evaded

Q: [507] vermischen
A: to mix, to mingle

Q: [508] verschieden
A: different, unlike

Q: [509] verstanden
A: (p.p. of: verstehen)
understood, comprehended

Q: [510] Verständnis
A: understanding

Q: [511] verstehen
A: to understand, to comprehend

Q: [512] Vertauschung
A: interchange, permutation, substitution

Q: [513] Verwechslung
A: confusion; exchange; mistake

Q: [514] Verzeichnis
A: list, register, index, table

Q: [515] via
A: by way of, via

Q: [516] vier
A: four

Q: [517] vierte
A: fourth

Q: [518] völlig
A: full(y), entire(ly)

Q: [519] vom
A: (= von + dem) from the, of the

Q: [520] von
A: from, of; concerning; by

Q: [521] vor
A: before.
liegt ... vor. See: vorliegen
kommt ... vor. See: vorkommen
(Cog., for(e))

Q: [522] vor-
A: (prefix) pre-, pro-

Q: [523] voran
A: (vor + an) before, ahead

Q: [524] vorangeschickt
A: (p.p. of: voranschicken)

Q: [525] voranschicken
A: (voran + schicken)
to send on before, to observe beforehand, to premise

Q: [526] voraus
A: before, in advance; previously

Q: [527] Voraussetzung
A: (voraus + Setzung) hypothesis, assumption

Q: [528] Vorbemerkung
A: (vor + Bemerkung) preliminary remark, introduction, preamble

Q: [529] vorhanden
A: at hand, available, existent;
-- sein, to exist

Q: [530] vorig
A: (vor + ig) previous, former

Q: [531] vorkommen
A: (vor + kommen) to occur

Q: [532] vorliegen
A: (vor + liegen) to be present, to be under consideration, to be at hand, to exist

Q: [533] Vorwort
A: (vor + Wort)
foreword, preface

Q: [534] wählen
A: to choose

Q: [535] wahr
A: true (cog., (Latin) verus; cf. verity, verily, veracious).

Q: [536] wäre
A: (imperf. subj. of: sein) were, would be;
wäre a = b, if a were equal to b (literally: were a equal b)

Q: [537] weg
A: away, off, gone

Q: [538] wegen
A: (sometimes follows the noun)
because of, for the sake of, with regard to, about

Q: [539] wegwerfen
A: to throw away, to reject

Q: [540] -weise
A: -wise, -manner

Q: [541] Weise
A: manner, way

Q: [542] welch
A: which, who, what, whose

Q: [543] wenden an
A: See: anwenden. (Cog., wind)

Q: [544] wenn
A: if, when

Q: [545] werden
A: to become, to be

Q: [546] werfen
A: to throw;
-- weg. See: wegwerfen

Q: [547] wie
A: how; as, such as

Q: [548] wieder
A: again

Q: [549] Wiederholung
A: repetition

Q: [550] wiederum
A: (wieder + um) again, in return, on the other hand

Q: [551] wir
A: we

Q: [552] wird
A: (3. sing. pres. of: werden) becomes, will be, is

Q: [553] wirklich
A: real(ly), true, truly, actual(ly), in fact

Q: [554] wo
A: where

Q: [555] wofern
A: (wo + fern) if, provided that

Q: [556] Wort
A: word, term, expression

Q: [557] Wortlaut
A: (Wort + laut) wording, text

Q: [558] wörtlich
A: verbatim, literal(ly), verbal(ly)

Q: [559] würde
A: (1. & 3. sing. subjunctive of: werden) would (be)

Q: [560] w.z.b.w.
A: abbr. (= was zu beweisen war),
which was to be proved, Q.E.D.

Q: [561] Zahl
A: number

Q: [562] zählen
A: to count (cog., tell; as in "all told", "every shot tells")

Q: [563] Zahlenpaar
A: (Zahlen + Paar) number pair

Q: [564] z.B.
A: abbr. (= zum Beispiel) e.g., for example

Q: [565] Zeichen
A: sign, symbol, mark (cog., token)

Q: [566] zeigen
A: to show, to demonstrate, to prove, to point out (cog., teach)

Q: [567] Zeile
A: line, row, range

Q: [568] zer-
A: (prefix) apart, asunder

Q: [569] zerlegen
A: (zer + legen) decompose

Q: [570] zu
A: to, toward (cog., to)

Q: [571] zugehörig
A: (zu + gehörig) belonging, appertaining, pertinent, proper

Q: [572] zugleich
A: (zu + gleich) at the same time

Q: [573] Zukunft
A: future

Q: [574] zulässig
A: admissible, permissible

Q: [575] zum
A: (zu + dem) to the, at the, for the

Q: [576] zunächst
A: (zu + nächste)
first of all, chiefly, to begin with, next to, nearest

Q: [577] zuordnen
A: (zu + ordnen) to assign, to make correspond

Q: [578] zurück
A: back

Q: [579] züruckführen
A: (züruck + führen) to lead back, to reduce to

Q: [580] zwar
A: (zu + wahr) indeed, certainly, truly, to be sure;
und --, namely, that is, and what is more

Q: [581] zwei
A: two

Q: [582] zweierlei
A: in two different ways, two different things

Q: [583] zweite
A: second

Q: [584] zweitens
A: secondly