无限小却无限大的集合 & 阶梯状的连续函数

    康托集合是闭区间[0,1]的子集,它的定义如下:给定区间[0,1],把这个区间分成三段,去掉中间那一端(即去掉(1/3,2/3)),然后把剩下的两段中每一段都按照刚才的方法再进行操作,然后再分,再分,就这样一直挖洞挖下去。在第二次操作后,剩下的区间是[0,1/9]∪[2/9,1/3]∪[2/3,7/9]∪[8/9,1],再操作一次后区间将由8段构成。最后剩下来的东西是什么呢?你能找到存在于这个集合中的某个具体的元素吗(不包括形如x/(3^n)的端点)?
    我们看到,n次操作后,区间的总长度为(2/3)^n,当n趋于无穷时,区间长度趋于0。但是这并不能说明这个区间里没有任何元素。事实上,我们可以找到至少一个元素。比如,下图中绿色的点表示三等分点,如果P满足AP/AB=A'P/A'B'的话,那么P点始终以比例相同的位置留在某一段上,这样的话即使无限地分下去也不会把它挖掉。
      
    P点的坐标可以通过解这个方程得到:x/1=(x-2/9)/(1/9)。解出来x为1/4。因此,1/4属于康托集合。当然,除了1/4之外还有很多点在这个集合内,我们只是找到了其中一个。事实上,康托集合内的元素有无穷多个。假如我们把所有0到1的数用三进制表示,那么我们发现,去掉的部分都是三进制小数里有数字“1”的。比如,第一次操作时,1/3和2/3的三进制分别是0.1和0.2,我们去掉的是所有从0.1到0.2的数(不包含端点,因为0.1也可以写成0.0222222222…)。第二次操作就去掉了百分位有1的那些数,依此类推。因此,只要一个位于0和1之间的三进制小数能够只用0和2写出,那么它就属于康托集合,因为它永远不会被去掉。刚才的1/4转化为三进制是0.020202…,因此它属于这个集合。显然,这样的数有无穷多个,比如三进制0.002002002…等于十进制的1/13,因此它也属于康托集合。同样,康托集合里不存在孤点,因为在它的左右可以找出无数个属于康托集合的数。应用对角线方法,这个集合里的元素居然还是不可数的。事实上,我们可以建立康托集合与闭区间[0,1]的一一对应关系。
    用以下方法可以把康托集合里的所有数与[0,1]的所有实数对应起来:将康托集合内的任意一个转化为三进制小数后,把每一个数字除以2,再当成是二进制小数转化回来。由于这些三进制小数里只含0和2,因此康托集合里的每个数都恰好能转化为一个[0,1]之间的二进制小数;同样地,二进制小数里的每个“1”变成“2”后也能得到一个康托集合里的数。
      
    设f为定义域在康托集合内的函数,定义f(x)为按照上面的转化方法x所对应的二进制小数,显然这个函数的值域就是[0,1]。比如1/3的三进制为0.0222…,而二进制0.01111…=0.1即十进制的1/2,因此f(1/3)=1/2。我们发现,2/3的三进制为0.2,而0.1的十进制也是1/2。于是f(1/3)=f(2/3)。类似地,那些被挖去的区间的两个端点对应的函数值都相同。现在,我们把这个函数的定义域也扩展到[0,1]:让康托集合里的那些被挖去的区间里的点的函数值与该区间对应的端点相同(在函数图象上看相当于把函数值相等的点用横线段连起来)。于是,f(1/2)=f(1/3)=f(2/3)=1/2,f(1/8)=f(1/9)=f(2/9)=1/4。这个函数一定是上升函数,它在长度为1的区间里从0增长到了1。同时,这个函数也是一个连续函数,因为康托集合与[0,1]的所有实数一一对应。这个函数是一个阶梯状的函数,但是它不是分段的,是连续的。它是无穷多个横线段组成的一个连续函数,除端点无意义以外导数值都是0。或者说,这个函数在不变之中上升。

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质数单词表

    我们可以使用36进制将所有的单词转化为数字。比如,(ADD)36 = (10×36^2+13×36+13)10 = (13,441)10。而13441是一个质数,因此我们说ADD是一个质数单词。
    下面列出了几乎所有的质数单词。

A

AAH ABANDON ABDOMEN ABDUCTED ABERRATION ABJURED ABLEST ABLUTION ABOLISH ABOMINATED ABORT ABORTIONIST ABOUNDED ABRIDGED ABRUPT ABSORB ABSTENTION ABSTRACT ABUTTED ACCEPT ACCEPTED ACCESSED ACCIDENT ACCLIMATIZATION ACCOMMODATION ACCREDITED ACID ACORN ACOUSTICIAN ACT ACTED ACUTEST AD ADAMANT ADD ADDUCTION ADJOINED ADMIXED ADORN ADULTHOOD ADVOCATED ADZ AERATED AFFORDED AFORESAID AFTERTHOUGHT AGNIZED AGRONOMIST AHEAD AIRED AIRIEST AIRMEN AKRON ALBEIT ALDERMEN ALEVIN ALLAYED ALLEGATION ALLEGED ALLERTON ALSIP ALVIN AMAH AMAZED AMENDED AMERINDIAN AMOEBOID AMPHIPLOID AN ANAPEST ANEROID ANGERED ANGOLAN ANIMATED ANIMATION ANNISTON ANNUALIZED ANODIZATION ANOINT ANTEED ANTICIPATED ANTITOXIN ANTITRUST AORIST APOGEAN APPALLED APPOSED AQUEDUCT ARCH ARGUMENT ARIGHT AROUND ARRAIGN ARROWHEAD ARTICLED ARYAN ASAP ASSASSIN ASSERT ASSERTED ASSESSED ASSEVERATED ASSN ASSUAGED ASSUMPTION ASTEROID ASTOUND AT ATHIRST ATOP ATT ATTENUATED ATTITUDINIZED ATTRACT ATTRIBUTION ATTRITED AUCTION AUDIENT AUDITED AUTOSUGGESTION AVANT AVIARIST AVIATION AVOCATION AVOIDED AVOUCH AVOWED AWED AWKWARD

B

B BABOONISH BACKDrop BAD BADINAGED BAGGIEST BAH BAIT BALANCED BALLOONIST BAN BANED BANGLADESH BANTERED BARB BARD BAREBACKED BAROGRAPH BARONET BASALT BASEBOARD BASILICAN BASINED BASSOON BATH BATON BATTEMENT BATTEN BATTENED BEACHHEAD BEAMIEST BEATEN BEATIFIED BECKON BECLOUDED BEETLED BEFUDDLEMENT BEGGARED BEGOT BEGUILED BEHOLDEN BEHOOVED BELAYED BELLIGERENT BEMUSEMENT BEN BENEATH BENNINGTON BEQUEATHED BERRIED BERWYN BESEECHED BETAKEN BETH BETTERED BEWITCHMENT BIBBED BIDDEFORD BIFURCATED BIGHEARTED BIKED BILKED BILLET BIPARTITION BIPED BIRTH BISCUIT BISECTION BITCH BITTED BITTEREST BIVOUACKED BLAB BLACKBIRD BLADED BLAH BLAIN BLIND BLINDED BLINDFOLDED BLITHEST BLONDEST BLOODIED BLOODSHOT BLOODSTAIN BLOWOUT BLOWZIEST BLUED BLUEFIELD BLUEPRINT BOB BOLD BOND BONNET BOOBED BOOED BOOKSHOP BOOST BOOT BOOZED BORON BORROWED BORSCHT BOSOMED BOTCH BOUNDED BOUT BOWED BRAGGED BRAN BRASH BRASHEST BRAWN BREAKFAST BREED BRIDLED BRIGHT BROADCASTED BROOD BROODIEST BROOKLYN BROTH BROWN BROWNED BUCKET BUD BUDDHIST BUILDUP BUILT BULKHEAD BULLETIN BULLHEAD BULLISH BULRUSH BUMP BUMPIEST BUN BUNION BURBLED BURIEN BURP BURRED BURT BUSHELED BUSIED BUSSED BUTTERFLIED

C

CAB CABARET CABIN CABINET CACHED CAESAREAN CAJOLEMENT CAKED CALMEST CALUMET CANAAN CANDID CANED CANON CAP CAPPED CARD CARET CARNATION CARP CARROLTON CARTLOAD CASEMENTED CATALOGED CATALOGUED CATALYST CATCHWORD CATECHIST CATECHIZED CATENATION CELLIST CEREBRATION CHAINED CHAMP CHAMPAIGN CHAMPION CHANSON CHAPLET CHATTED CHAUFFEURED CHEAP CHEAPENED CHEAPEST CHEAPIST CHECKED CHEVRON CHEWIEST CHICKWEED CHIFFON CHILD CHILDBIRTH CHINTZ CHIRRUP CHISELLED CHLORINATION CHOP CHOPPIEST CHORTLED CHRONOLOGIST CHUNKIEST CHURCHMANSHIP CHURNED CIRCUITED CIT CLACKED CLAMPED CLAP CLEARED CLEAT CLENCH CLERGYMEN CLINCH CLINGIEST CLOSEMOUTHED CLOTHESPIN CLOUDED CLUMPIEST CLUTCH CLUTCHED COAGULATED COALITION COARSEST COAXED COB COBWEB COBWEBBED COFFEEPOT COGNITION COIL-START COITION COLLATERALIZED COLLIMATED COMB COMMANDANT COMMENCED COMMENT COMMISSION COMMITTEEMEN COMMUNION COMPANION COMPENSATED COMPLAISANT COMPLIMENTED COMPOSITION CONCERNMENT CONCERT CONCESSION CONCOCTED CONCUSSION CONDEMNED CONDITIONED CONDUCT CONED CONFECTION CONFIDANT CONFINED CONFLICTION CONFOUNDED CONFUCIAN CONGEALMENT CONGEST CONGESTED CONGRATULATION CONGREGATED CONJOIN CONJURED CONNED CONSECRATION CONSENT CONSOLIDATED CONSTITUTED CONSUMED CONTEMPLATED CONTEST CONTEXT CONTINUATION CONTRIVED CONVOLVED COOKOUT COON COOPERATED COPENHAGEN COPILOT CORDON CORELATED CORINTHIAN CORNISH CORP CORRELATION COSMONAUT COSTUMED COUGH COULDN'T COUNCILMEN COUNTERFEITED COUNTERMAND COVENANT COVERT COWBIRD COWMAN COZ CP CRAWFISH CREMATION CREPT CRIB CRIMPED CRITERION CROTCH CROWD CRT CRUCIFIED CRUD CRUMPET CRUSHED CT CULT CUMQUAT CUP CURATORSHIP CURBED CURED CUSHIONED CUT CUTEST CYAN CYST CZ

D

D DAFFIEST DAMN DAMOCLEAN DAMPEN DAN DANDIFICATION DANDIFIED DANISH DANKEST DARTED DARWINIST DAUB DAVIT DAWN DAZZLED DB DEADBEST DEBAUCH DEBAUCHED DECADENT DECAPOD DECEIVED DECOMPRESSED DECOYED DEFERRED DEFIED DEFLATED DEFLECT DEFOREST DEGENERATED DEIST DELTOID DEMANDED DEMOLISHED DEMON DEMONSTRATION DENOMINATION DENT DENTED DEODORANT DEPARTMENT DEPEND DEPICT DEPOLARIZATION DEPORTATION DERELICT DERVISH DESICCATED DESOLATED DESPONDENT DESTINATION DETACHED DETERMINANT DETERRED DETONATION DEVEST DEVESTED DEVOTION DEVOURED DEVOUT DID DILAPIDATION DILATED DILATION DIMMEST DIMOUT DIMWIT DIN DINED DINT DIPLOMAT DIRTIEST DISALLOWED DISASSOCIATION DISCIPLESHIP DISCOMFORT DISENCHANT DISENTANGLEMENT DISFRANCHISED DISFRANCHISEMENT DISGUST DISHEARTENMENT DISINTEREST DISINTERMENT DISMOUNTED DISOBLIGED DISPATCHED DISPUTATION DISRESPECT DISSIPATION DISTAIN DISTRAIN DISTRICTED DIVED DIVVIED DIXIELAND DJ DOBERMAN DOCKETED DOCUMENTATION DODGED DOESN'T DOGFISH DOGSLED DOLLIED DOLPHIN DOMINATION DON'T DOORSTEP DOTHAN DOUBTED DOWDIEST DOWNIEST DOWNRIGHT DOWNWARD DOYEN DOZ DOZEN DRAB DRABBED DRAFT DRAFTSMAN DRAMATIST DRAT DRIEST DRIFT DROWSED DRUID DRUNKARD DUB DUCAT DUCKED DUET DUMONT DUMPED DURST DWARFED DWELT DYED DYNAST DYSFUNCTION DZ

E

EAGLET EARTH EASED EAST ECLAT ECOLOGIST EDEN EERIEST EFFERENT EFFORT EFT EH EIGHTH EIGHTIETH EJECTION ELAN ELECTROPLATED ELEVATION ELIZABETHAN ELOQUENT EMASCULATION EMBALMED EMBALMMENT EMBOLDENED EMBRACEMENT EMIGRANT EMIT EMITTED EMPATHIZED EMPTIEST ENAMELED ENCODED ENCORED ENCRYPT ENDICOTT ENERGIZED ENFIELD ENGENDERED ENGROSSED ENHANCEMENT ENID ENLIVENMENT ENNOBLED ENROLMENT ENSCONCED ENSHRINED ENTOMB ENTRAP ENTREAT ENTRENCHED ENWIND ENWRAPPED EON EPITOMIZED ERSATZ ESCHEAT ESCROWED EST ETCHED EVACUANT EVALUATED EVANESCENT EVENT EVICT EVICTION EVOLUTION EVOLVEMENT EXCLAIMED EXCLAMATION EXCUSED EXECRATED EXEMPLIFIED EXEMPT EXHILARATED EXHILARATION EXILED EXISTED EXIT EXITED EXPECTORATION EXPENDED EXPIRED EXPLOIT EXPORT EXPORTATION EXPRESSION EXPURGATED EXTERMINATION EXTINCTION EXTOLMENT EXTORT EXTROVERSION EXTRUSION EYEWASH

F

FABRICATED FACT FACTIONALIST FAD FAIR-TRADED FAIRYLAND FAITH FAKED FALSIFIED FASCINATED FASTED FASTEST FAUN FEINT FELON FERGUSON FERMAT FERMENTED FERRIED FERVID FETID FETISH FEZ FICKLEST FID FIERIEST FILL-IN FILLIP FINNED FIORD FIREBOAT FIREFIGHT FIREPROOFED FIRMED FISTED FIT FIXED FLAB FLATBED FLATBOAT FLATTED FLATTOP FLESHED FLIED FLIP FLIPPANT FLIT FLITTED FLOCCULENT FLOODLIGHT FLOWERPOT FLOYD FLUID FLUORIDATED FOCALIZATION FOLD FONDANT FOOD FOOTSTEP FORECAST FOREMEN FORESTED FOREWARN FOREWARNED FORFEITED FORMALIZATION FORMAT FORNICATION FORSOOTH FORTIETH FOURFOLD FOXED FRAGMENTED FRANKLIN FRAUGHT FRAYED FRENCHMAN FREON FREQUENT FRESH FRESHEST FRINGIEST FRIZZIEST FROGMAN FROGMEN FRONT FROTHIEST FROWNED FRUCTIFIED FT FUD FUELLED FUN FUNDED FUNNED FUNNELLED FUSSED FUSTIEST

G

GAB GADSDEN GALLIVANT GALLOP GALVANIZATION GAMIEST GAMUT GANGED GANGLAND GAP GARAGED GARISH GARMENT GARRET GASIFIED GASP GAUD GAUGED GAUNTEST GELATIN GELD GENT GEORGIAN GERALD GERARD GERRYMANDERED GERUND GET GETUP GHETTOIZED GHZ GIGGED GIGGLED GILBERT GIMP GIN GIRTH GLARED GLEN GLOP GLUT GNAT GNAWN GNP GOAT GOB GOD GONAD GOODHEARTED GORDON GOUT GP GRAD GRAINED GRANDILOQUENT GRANDSON GRAPHED GRAVELED GRAVEN GREAT GREEN GRID GRIDDED GRIND GRISTLIEST GROOVED GROSSEST GROT GROTON GROUPED GROWNUP GRUDGED GUARANTEED GUARD GUARDSMEN GUDGEON GUEST GUIDED GUIDON GUMMIEST GUMPTION GUN GUNMAN GUNSMITH GUTTED

H

H HACKLED HADN'T HAGGISH HAH HAIRED HALLOWEEN HALOED HAMMERHEAD HAMPERED HANDGUN HAND-ME-DOWN HANDOUT HANDWOVEN HANDYMEN HARD HARDHEADED HARPSICHORD HART HARTFORD HARVEST HASN'T HASTED HATBAND HAUNCH HAVERFORD HAWAIIAN HAWKWEED HAYWARD HEARKENED HEART HEARTBURN HEARTEN HEAVENWARD HEBRON HECATOMB
HE'D HEDGED HEFTED HEIGHT HELEN HELLBROTH HELLCAT HELMETED HEMMED HEMOSTAT HENCEFORTH HERBERT HERD HEREIN HICCUP HIGH HIGHEST HIGHHANDED HIGH-PRESSURED HIGHT HILLCREST HILLIEST HIND HINDERED HINDSIGHT HINGED HINT HIT HOARSEN HOB HOCKSHOP HOED HOGSHEAD HOGWASH HOISTED HOLDOUT HOLLAND HOLLOWED HOMEBOUND HOMEGROWN HOMESTRETCH HOMIEST HONEYCOMBED HONIED HOOCH HOP HOPPED HORSED HORTICULTURIST HOTCHPOT HOTHEAD HOUNDED HOUSEBOAT HOUSEBROKEN HT HUDDLED HUFFED HUFFIEST HUGGED HULLED HUMANKIND HUMBLEST HUMPH HUNCHBACKED HUNT HURLED HURRAH HURT HUSH HUSTLED HUTCHINSON HYPED HYPERTROPHIED HYPNOTIST HZ

I

IAMB IB ICELAND ICONOCLAST ID IDIOT ILLUMINATED ILLUSION IMITATED IMMOLATION IMMURED IMPAIRMENT IMPALED IMPART IMPERSONATED IMPLEMENT IMPORTANT IMPOTENT IMPRINT INACTIVATED INCRUST INCUBATION INDEMNIFIED INDIRECTION INDUCED INEDITED INEXISTENT INFANT INFLECT INFLECTED INFRACT INFRACTION INGROWN INHERIT INHIBIT INKBLOT INKSTAND INMOST INN INNERVATED INPUTTED INSCRIBED INSECT INSIST INSTRUMENTALIST INSULTED INTERACT INTERBRED INTERCEPT INTERCEPTED INTERCONNECTION INTERDEPENDENT INTERESTED INTERFERON INTERLARDED INTERLOCUTION INTERRUPT INTIMIDATED INVEIGH INVERSION INVIGORATED INVIGORATION INVOKED IRAN IRRELIGION IRRIGATED IRRITATION IRRUPTED IT IVAN

J

J JABBED JABOT JACKETED JANGLED JAUNDICED JAUNT JAUNTED JAVELIN JAWED JAZZ JEEP JERKIN JILT JINN JOAN JOCUND JOHNSON JOLT JOSTLED JOYPOP JUDGMENT JUICED JUKED JULIAN JUMP JUNCTION JUT

K

KAPH KAPUT KAT KEELBOAT KEELSON KEEN KENTWOOD KENYON KETCH KEYPUNCHED KIBBLED KILOBIT KIN KIND KINDLED KINGBOLT KINGLET KINGPIN KINSHIP KIRKLAND KIT KITED KLATCH KLUDGED KNELT KNISH KNOBBIEST KNOWN KNUCKLEHEADED KOBOLD KOLITSCH KRUGERRAND KUMQUAT KURT

L

LAGOON LAID LAIN LAKED LAMBASTED LANDED LASED LASERJET LASHED LATIN LAUREATION LAYTON LEAFIEST LEAFLET LEAPT LEAST LED LEEBOARD LEERED LEEWARD LEGALIZATION LEGGIEST LEGION LEGITIMIZED LEND-LEASED LENGTHIEST LENSED LENTEN LEOTARD LEPRECHAUN LESSEN LEST LET LEV LEVERED LIAISON LIBBED LIBYAN LIED LIEN LIFE-SIZED LIKENED LILT LIMB LIMIT LIMPET LINDENWOLD LINEAMENT LINEMAN LINEN LINEUP LINNAEAN LIONIZED LIPPED LISP LIST LIT LIVID LOBATED LOCATED LOGAN LOLLED LOMBARD LONGED LONGWOOD LORDSHIP LOST LOT LOTION LOUD LOUSIEST LUCKIEST LUGLUGGED LUMBERTON LURID LUST LYNNWOOD

M

MAIDENHOOD MAIMED MAJORED MALLARD MANDATED MANIFEST MANSION MARKED MARKET MARMOSET MARRIED MARSH MARSHIEST MASHED MAT MATURATION MAUDLIN MAXIMALIST MAYWOOD MAZED MAZIEST MEADOWSWEET MELIORATED MELTED MENTION MERCHANTMAN MERCURATED MERGED MESHED MESMERIST MESSIAH MESSIEST METED MICHIGAN MICROFILMED MID MIDMOST MIGHT MIGRATION MILBURN MILEPOST MILKMAID MILKMAN MILQUETOAST MILTON MISANTHROPIST MISCEGENATION MISCONDUCT MISCONSTRUED MISCREANT MISDIRECT MISFILED MISGUIDED MISQUOTED MISTRUST MISTYPED MISUSED MOAN MOB MOD MODELED MOIST MOISTEN MOLDED MON MONETIZED MONGOLIAN MONIST MONITION MONITORED MONKEYED MONOVALENT MOOED MOON MOONLIGHT MOONLIGHTED MOP MORTON MOTH MOTTLED MOUNT MOUSIEST MOUTHED MOUTHWASH MOWN MPH MT MULCT MULISH MULLION MULTIMILLION MULTIPLICAND MULTIPRONGED MUNCH MURED MUSHED MUSHIEST MUSTERED MUTANT MYCOLOGIST MYELIN MYOSIN

N

N NAT NATION NAUGHTIEST NEAP NEAPOLITAN NEED NEGLIGENT NEST NET NEUROLOGIST NIB NIGGARD NIGH NIGHTSHIRT NIMCOMPOOP NOBBIEST NOBBLED NOBELWOMAN NOBLEWOMAN NONACID NONACQUISITION NONCITIZEN NONCONSIDERATION NONDESCRIPT NONFAT NONMEMBERSHIP NONRESISTANT NONSLIP NORMALIZATION NORMAN NOSH NOURISH NOV NOVEMDECILLION NTH NUDIST NUN NURTURED NV

O

OARED OBEISANT OBFUSCATED OBJECT OBSCURANTIST OBSOLESCENT OBSTETRICIAN OBTRUSION OCCULT OCCULTATION OCHERED OCTANT OCTET OCTODECILLIONTH OD ODIN OFFERED OFFHAND OFFPRINT OH OILBIRD OLD OLDEST OLDISH OMELET OMIT ON ONRUSH ONSET ONSLAUGHT OPENED OPPRESSED OPTION OPULENT orBITED orCHESTRATED orCHID orDAINED orDERED orEGON orLAND OTHERWORLD OUCH OUST OUT OUTCROP OUTFITTED OUTLAST OUTLASTED OUTPUT OUTSHOUT OUTSIT OUTSMARTED OUTSPEND OVEN OVERCONFIDENT OVERDRIVEN OVERINDULGED OVERMATCHED OVERRAN OVERSKIRT OVERSOFT OVERTRUMP OXEN OXYHEMOGLOBIN

P

PACED PACKED PAGED PAGINATED PAIN PAINED PAIRED PALEONTOLOGIST PALLED PALMIST PALTRIEST PAMPHLET PAN PANNED PARATROOP PARCELLED PARCHMENT PARKLAND PARRED PARRIED PARROT PARROTED PARTED PAST PASTELIST PAT PATCH PATIENT PATRON PATRONIZED PAWTUCKET PAYED PAYLOAD PEALED PEANUT PEAT PEBBLED PECTIN PECULATION PEDANT PEDESTALLED PEDIATRIST PEELED PEEN PEERED PEEVED PELLET PELLETED PELT PELTED PENDED PENETRATION PEOPLED PEPPERED PERAMBULATION PERFORMED PERILED PEROXIDED PERSIST PERSON PERSUASION PERVERT PET PETULANT PHONED PHONETICIAN PHYSIOGNOMIST PIGGED PIN PINED PINFISH PINIONED PINKEST PINNACLED PINNED PINPOINTED PIP PISTOLLED PITCHOUT PITH PLAID PLAIT PLANCHET PLANET PLANTAIN PLANTATION PLASTID PLATTED PLAYFIELD PLAYPEN PLOD PLUMB PLURALIZED PLUSH POET POINTED POLAND POLAROID POLLINATION POLYGAMIST POMADED POMP POMPON POMPTON POOCH POP PORIFERAN PORTENT POSED POSIT POSTPAID POSTULATION POTION POTTSTOWN POULTICED POWERED PREDICAMENT PREDICATION PREDISPOSED PREDOMINATED PREEXIST PREEXISTENT PREFECT PREFERRED PREFIGURED PREHEAT PRESERVED PRETTIEST PREVAILED PREVARICATION PREVIEWED PRIED PRIMETEST PRIMMED PROCTOLOGIST PROCURED PROD PROHIBIT PROMOTION PRONOUN PROSED PROSPECT PROSTRATED PROTON PROTRACT PROVOKED PROWLED PT PUBESCENT PULLED PULLMAN PULP PULVERIZED PUMPKIN PUN PUNISH PUNNED PURDAH PURIST PUTOUT PUTT PYTHON

Q

QED QUIESCENT QUIET QUIETEST QUINTUPLED QUIP QUOIN QUOIT

R

RABBET RACIST RADICALIZED RADIOCARBON RADIOLOGIST RADON RAFT RAGGED RAGOUT RAID RAIN RAINSPOUT RAMBLED RAMJET RAMMED RANKED RAPPED RAT RATION RATLIN RATTRAP RAUNCHIEST RAVELMENT RAVISH REACT READIED READOPT READORN REAPPEARED REARMED REARRANGEMENT REATTACH REATTEMPT REBIND REBOUNDED REBUILD REBUTTED RECALCITRANT RECALCULATION RECALLED RECLAIMED RECOIN RECOLORED RECONFIRMATION RECONSIDERATION RECOUNTED RECRUDESCENT RED REDD REDEMANDED REDESCEND REDIRECTION REDOUBLED REDSKIN REED REEDIEST REEKED REENACT REFITTED REFLOURISH REFORMED REFRACTION REFRAIN REFROZEN REFURNISH REFUSED REFUTATION REGENERATED REGIMENT REGIMENTATION REGRANT REGRETTED REHEATED REIMPLANTED REIN REInsertED REINSTALLED REINVITED RELAPSED RELICT RELIGHT RELOCATION RELUCTATED REMANDED RENT REP REPAINTED REPAIRMAN REPASSED REPLANTATION REPLENISH REPOLISH REPORT REPROACH REPROBATION REPUBLISH REPUTATION REPUTED RERUN RESECTED RESH RESINATED RESONANT RESORTED RESOWED RESPECT RESPECTED RESPIRED RESTART RESTAURANT RESTRICTION RESURGENT RETAIN RETCH RETEST RETOOLED RETRACED RETRIEVED RETURNED REUNIFICATION REV REVALUATION REVAMPED REVELED REVERT REVIVED REVOLT RHEUMATOID RHOMB RHYMED RICHLAND RICHMOND RIDERSHIP RIDGEFIELD RIND RIVED RIVEN RIVETED ROD ROILED ROILIEST RON RONALD ROOKED ROOSTED ROOTED ROUGH ROUGHEN ROUNDEST ROUNDLET ROUTED ROVED ROWELLED RUB RUBICUND RUDIMENT RUDOLPH RUFFED RUGGED RUNAROUND RUNDOWN RUNT RUSHIEST RUSSET RUTH RUTHANN RUTTED

S

SACRED SADDEN SAFEGUARD SAGGED SAILED SALAD SALESWOMAN SALT SAMOAN SAN SANDBLAST SANDED SANDWORT SAPPIEST SASH SAT SAUNTERED SAWFISH SAXHORN SB SCABBED SCAFFOLD SCALLION SCALP SCAN SCARFPIN SCATTERED SCHMALTZ SCHMALTZIEST SCHOOLED SCOOP SCOOTED SCORECARD SCOT SCOTSMAN SCRAGGIEST SCRAMMED SCRAPED SCREECHIEST SCREED SCRUBBED SCRUNCH SCULLED SCULPTED SCULPTURED SCUMBLED SCUMMED SCUTCH SD SEABIRD SEALSKIN SECTARIAN SEDATED SEEDED SENSATIONALIST SENTIENT SEQUENCED SERIALIST SERIALIZED SERVICED SESAMOID SET SEVENTY-SIXTH SEXAGENARIAN SEXTANT SEXTILLION SEXTUPLED SHAH SHAN SHAPEUP SHARED SHEEN SHELVED SHIP SHIRTWAIST SHOD SHOED SHOPPED SHORED SHOREFRONT SHORTEN SHORTHAND SHOTTEN SHOVELLED SHOWN SHREWD SHRIVELLED SHUDDERED SHUNNED SHUNT SHUT SIB SIDEBOARD SIDEMAN SIDESPIN SIEGED SIEVED SIGNALMAN SIGNET SIGNPOST SILKEN SILKIEST SILUROID SILVERSMITH SINEWED SIPPED SIRRAH SIZZLED SKEIN SKID SKILLET SKIN SKINTIGHT SKULKED SKYLIGHT SLAGGED SLANDERED SLAVISH SLED SLEDDED SLEEKEN SLENDEREST SLIPKNOT SLIPPED SLITHERED SLOPPIEST SLOT SLOVEN SLUBBED SLUGGED SLUICED SLUMPED SLURP SMART SMEARED SMIDGEN SMILED SMI
RCH SMITH SMOKED SMUT SNAP SNATH SNEAKED SNIGGERED SNITCH SNOUT SNUB SOAPED SOAPIEST SOARED SOBERED SOBERIZED SOCIALIZED SOFT SOLARIZATION SOLATION SOLD SOLEMN SOLEMNIZED SONANT SONNETIZED SORPTION SORT SOT SOWN SPACEBAND SPACKLED SPARKIEST SPARTAN SPAT SPEARMAN SPECIATED SPECTATED SPELTZ SPEND SPHEROID SPIKELET SPILT SPLINTERED SPOKED SPOOLED SPOONED SPORRAN SPOT SPOUSED SPREAD SPRINGIEST SPURT SQUALID SQUAT SQUEALED SQUEEGEED SQUELCH SQUIB SQUIBBED SQUIFFED SQUIRISH SQUIRRELED STABBED STALINIST STALLED STALLION STALWART STAMPED STANCHION STANDARD STANDPOINT STAPHYLINID STEADFAST STEADIEST STEPCHILDREN STERILANT STERN STICKMAN STICKUP STIMULATED STIRRED STOCKIST STODGIEST STOLEN STOMATILOGIST STONEWALLED STOUTENED STOUTEST STP STRAGGLIEST STRAIT STRANGEST STRAPPED STRAWBOARD STREAMWOOD STREET STREWN STRIDENT STRIKEBOUND STRINGBOARD STRIPT STROLLED STRONGMAN STROWN STUDENTSHIP STUFFIEST STULTIFICATION STUMPIEST STYED SUB SUBEDIT SUBINFEUDATED SUBJACENT SUBLATION SUBREGION SUBSCRIBED SUBSTANDARD SUBTENANT SUBTITLED SUCKED SUDSIEST SUET SUFFRAGIST SUGARED SULFONATED SULFURETED SUMMARIZED SUMMED SUNDERED SUNKEN SUNLAMP SUPERADDITION SUPERCONDUCT SUPERINTEND SUPERMARKET SUPERVENTION SUPINATION SUPPOSED SUPPRESSED SUPPURATION SURROUNDED SUSPECT SUSPECTED SWAB SWAGMAN SWAIN SWAMP SWAN SWANNED SWASHBUCKLED SWATH SWAYED SWEETEST SWERVED SWIRLED SWITCH SWOT SYMBOLED SYNCH SYNCOPATED SYNOD

T

T TABBED TABLESPOON TACH TAD TAGSTART TAINT TAJ TALKATHON TALLISH TAMP TAMPION TAN TANKED TANTALIZATION TANZANIAN TARBUSH TARGETED TARN TARPAULIN TARTLET TAUNTED TAUTENED TAVERN TAXED TAXICAB TAXIDERMIST TEARDrop TECHED TECHNICALIZATION TEENIEST TEGUMENT TELEGRAPH TELEOSTEAN TELETYPED TENANT TENET TENSION TENTED TEPID TERREPLEIN TERRORIZED TESSERACT TEUTON TH THEGN THEORIST THEURGIST THEY'D THIEVED THIEVISH THIN THINCLAD THIRDHAND THISTLEDOWN THOUGHT THOUSAND THREADIEST THRIVEN THRUMMED THYROCALCITONIN THYROID TICKETED TICKLED TIDBIT TIFFED TIGERISH TILT TILTH TIMBERED TIMEOUT TIMIDEST TINCT TINGED TINIEST TINKLED TIT TOAD TOADIED TOASTIEST TOBOGGANIST TOD TODDLED TOEHOLD TOFT TOLERANT TOLERATED TOMCOD TONED TONSURED TOOTHBRUSH TOPNOTCH TORRENT TORRID TOTALITARIAN TOTIPOTENT TOURED TOWBOAT TOWHEADED TOWN TOWNSWOMAN TOXICANT TOYON TRACTION TRADESMAN TRAINBAND TRAIPSED TRAMMELED TRANSECT TRANSFIXION TRANSHIP TRANSPORT TRANSPOSED TRAUMATIZED TRAVAILED TRENCHANT TRESPASSED TRICKISH TRICORNERED TRIDENT TRIFLURALIN TRIGGERMAN TRIGLYPH TRIJET TRILLED TRIPLICATED TRIPLICATION TRISTEARIN TRIVET TROLLEYED TROLLOP TROOP TROOPED TROUBLED TRUCKLED TRUCKMAN TRUDGED TRUEST TRUMPET TRUST TUBIFICID TUCKERED TUCKET TUFT TUGBOAT TURBINATED TURBORAMJET TURD TURNED TURNOUT TURRET TURRETED TUSCAN TUSSAH TUT TWENTY-FIRST TWIGGED TWILLED TWIN TWIXT TYPESET TYROCIDIN TYROTHRICIN

U

UCB UGLIFICATION UMBILICATION UMLAUT UMPTEEN UN UNABBREVIATED UNABSORBED UNACCOMMODATED UNACCOMPLISHED UNACCUSTOMED UNAMAZED UNAMBIVALENT UNAMPLIFIED UNANELED UNANIMATED UNAPPRECIATION UNASSUAGED UNATTESTED UNAVOWED UNAWED UNBAKED UNBARBED UNBEKNOWNST UNBELT UNBIGOTED UNBLOWN UNBLUNTED UNBOLT UNBURNISHED UNBURNT UNCAGED UNCILIATED UNCOFFINED UNCOMPLETED UNCONCERN UNCOUPLED UNCREASED UNCRITICIZED UNCROSSED UNCROWDED UNCURDLED UNDEAD UNDEEDED UNDEFACED UNDEFENDED UNDELIVERED UNDERACT UNDERBRED UNDERFED UNDERVALUED UNDERWEIGHT UNDIAGNOSED UNDIGESTED UNDIGNIFIED UNDILATED UNDISTRACTED UNDIVERSIFIED UNDOCKED UNDOCUMENTED UNDULATED UNENGAGED UNENTANGLED UNENVIED UNESCORTED UNEXAGGERATED UNEXPIRED UNFANNED UNFATHERED UNFEDERATED UNFETTERED UNFLAWED UNFLEXED UNFRIEND UNFROZEN UNFUSED UNGIRD UNGIRT UNGLAMORIZED UNGLAZED UNGRASPED UNHANGED UNHARMED UNHEARD UNHIRED UNHUNTED UNIMAGINED UNIMFLECTED UNIMPLEMENTED UNIMPROVED UNINTERESTED UNION UNIONIZED UNIONTOWN UNISON UNITIZATION UNIV UNJADED UNJOINT UNJUST UNLADED UNLEVIED UNLICKED UNLINED UNLIST UNLIT UNLOAD UNLOOSENED UNMAN UNMARRED UNMENTIONED UNMONEYED UNMOVED UNNOTED UNOBLITERATED UNPADDED UNPARALYZED UNPARDONED UNPARTED UNPARTITIONED UNPERVERTED UNPLASTERED UNPRACTICED UNPRESSED UNPRINCIPLED UNPROSTITUTED UNPURGED UNQUESTIONED UNRATED UNRECLAIMED UNREDEEMED UNREELED UNREEVED UNRESERVED UNREVEALED UNRIVALED UNROASTED UNSCATHED UNSETTLEMENT UNSHELLED UNSNAP UNSOPHISTICATED UNSPLIT UNSPOKEN UNSTAINED UNSTUDIED UNSWEPT UNTAMED UNTAPPED UNTHATCHED UNTORN UNTREAD UNUSED UNUTTERED UNWEARIED UNWEDDED UNWISH UNWOVEN UNWROUGHT UPPED UPSHIFT UPSHOT URINATION UROCHORD UROPOD USURPED UT UTAH UTMOST UTOPIAN

V

V VACUOLATED VACUUMED VALANCED VALUATED VAN VAPID VAPORIZATION VAPORIZED VASOTOCIN VAULT VAULTED VAWARD VD VEHEMENT VELD VENDITION VENERATION VENTED VERSIFICATION VERT VESICATION VESTIBULED VET VETERINARIAN VEXILLOLOGIST VICED VIDICON VILLAIN VINEGARISH VINELAND VIP VISAED VISED VISION VISITANT VITIATED VIVANT VIVERRID VIVID VOLANT VOMITED VOTED

W

WAFTED WAILED WAIN WAISTCOATED WALKOUT WAMBLED WANGLED WANT WANTON WARED WARIEST WARRANT WASH WASHBOARD WASHWOMAN WATCHBAND WATCHED WATERIEST WATERWORN WEEN WELKIN WELT WEN WEND WESLEYAN WESTERN WESTFIELD WESTPORT WETLAND WHALED WHAT WHEATEN WHELP WHINED WHIP WHIRRED WHIST WHITEHEAD WHITETHROAT WHOLESALED WIDEST WIDTH WIEFERICH WIENERWURST WIFEHOOD WIGEON WIGGED WILDWOOD WINCH WIND WINDBURNED WINDSCREEN WINESHOP WIREMAN WITCH WITHOUT WITTIEST WOAD WOLCOTT WOMAN WOMB WON WONDERMENT WONT WOODENHEAD WOODLOT WOOLSHED WORKMEN WORKUP WORRYWART WORSEN WORSTED WORTHINGTON WOULDN'T WOULDST WRESTED WRETCH WRIT WT WYLIECOAT WYND

X

XENOLITH XYLOGRAPH

Y

YACKED YAMEN YAP YARDMAN YARN YD YEASTIEST YELLED YIDDISH YIELDED YOGHURT YOU'D

Z

ZEN ZENITH ZEST ZONATED ZOOPLANKTON

参见:http://primes.utm.edu/notes/words.html