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How big is infinity? - Dennis Wildfogel

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View full lesson: http://ed.ted.com/lessons/how-big-is-infinity Using the fundamentals of set theory, explore the mind-bending concept of the "infinity of infinities" ...

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irrational rational ratios fractions infinity numbers whole numbers decimals Kantor sets of numbers unanswered questions mathematics math TED-Ed TEDEducation TED Education Augenblick Studios Georg Cantor whereby whence wherewith cause how motive mystery proof by which through which at which point in what respect where why wherein H.O.W. 'how' HOW How huge full hefty fat vast ample bulky bull burly husky jumbo packed roomy awash mondo teeny tiny blah baby little minute small slight thin poor bland dull infant humble shy itsy leading popular serious main eminent prime super weighty minor tall adult elder mature free heroic lofty noble arty haughty pompous proud A-OK adequate admissible all right average big common cooking with gas cool copacetic decent delightful fair hep hip hunky-dory in the swim kosher large okay on the ball on the beam passable peachy keen pleasant pleasing respectable right on standard sufficient swell tolerable trendy unexceptional unobjectionable up to code up to snuff welcome Robin Hood all heart benevolent big-hearted bleeding heart charitable considerate generous good good scout human humane humanitarian kind magnanimous openhanded philanthropic self-sacrificing abounding abundant bounteous bountiful broad capacious commodious copious enough expansive extensive galore great heavy lavish liberal no end plenteous plentiful plenty profuse rich spacious spare substantial unrestricted voluminous wide altruistic beneficent benign caring chivalrous compassionate helpful kindhearted tenderhearted warmhearted well-disposed arrogant big-headed bombastic cocky conceited crowing egotistic egotistical exultant full of hot air hifalutin hot stuff know-it-all loudmouth on ego trip pretentious puffed-up self-aggrandizing self-applauding smart-alecky snooty strutting stuck-up swaggering swanky swollen-headed vainglorious vaunting windbag awkward beefy colossal cumbersome cumbrous enormous gross high hulking immense long mammoth massive ponderous unhandy unmanageable unwieldy acceptable boastful Big B.I.G. B.I.G infinity Infinity Dennis dennis insane crazy stupid wrong absurd unwise wild loony raving silly flaky mad nutty wacky freaky kooky sane wise stable sound well smart batty campy daffy dippy fooling around foolish for grins gagged up goofy idiotic illogical inane incongruous irrational jokey joshing laughable ludicrous nonsensical off the wall preposterous sappy screwy tomfool unreasonable approximate capricious discretionary erratic fanciful frivolous inconsistent injudicious irresponsible offhand optional random subjective supercilious superficial unaccountable unscientific wayward willful abominable animal barbarous base bestial boorish brutal brute brutish carnal coarse cruel degraded depraved disgusting feral ferine foul gluttonous gross inhuman loathsome low monstrous obscene piggish prurient repulsive sadistic swinish unclean vile hasty heedless impetuous inconsiderate mindless rash reckless senseless shortsighted thoughtless unseeing unthinking violent aberrant bewildered confused crazed demented deranged deviant deviate disarranged disordered distracted disturbed flipped flipped out hallucinatory incoherent lightheaded lunatic maniac maniacal manic off one's head out of one's head out of one's skull rambling unhinged unsettled wandering ape baked bananas berserk cracked delirious disconcerted displaced dotty frantic frenzied fried loco maddened nuts perplexed schizzo unbalanced unglued unscrewed unsound unzipped whacko arbitrary beastly blind Irrational wise normal lucid logical sane stable prudent sober knowing sound calm cool unwise foolish stupid insane idiotic unstable excited agitated unsound confused careless acceptable allowed applicable appropriate concedable fair fitting just justifiable lawful legal legitimate licit likely not impossible not unlikely okay passable permissible permitted pertinent possible probable proper rational reasonable relevant right suitable tolerable tolerated warranted worthy cogent conclusive detailed diagnostic discrete dissecting explanatory expository inquiring inquisitive interpretive investigative judicious organized penetrating perceptive perspicuous precise problem-solving questioning ratiocinative scientific searching solid studious subtle systematic testing thorough valid well-grounded able to hold water assertable believable conceivable credible defendable defensible feasible imaginable maintainable supportable sustainable viable workable aboveboard authentic colorable convincing credential creditable fiduciary honest-to-god impressive persuasive plausible presumable presumptive reliable satisfying straight supposable tenable tried trusty unquestionable up front able adept adroit alert apt astute brainy brilliant cagey canny capable competent crackerjack cunning deep dexterous/dextrous discerning egghead expert foxy gifted good handy intelligent inventive keen knowledgeable many-sided nimble nobody's fool pretty pro qualified quick quick on trigger quick-witted resourceful sagacious savvy sensible sharp shrewd skilled skillful slick sly smart sprightly talented versatile witty articulate comprehensible consistent identified intelligible meaningful orderly reasoned admissible analytic arguable clever coherent Rational rate scale quota whole allegory analogizing analogy analyzing association balancing bringing together collating collation comparability connection contrast correlation discrimination distinguishing dividing estimation example exemplification identification illustration juxtaposition likeness likening measuring metaphor observation opposition paralleling ratio relating relation resemblance segregation separation similarity testing weighing amount amplitude caliber dimension division expanse extent gauge gradation grade height intensity interval length limit line link mark notch period plane point proportion quality quantity range reach rung scope severity shade size space stage stair standard step stint strength tenor term tier bit fragment part partial piece portion quotient section segment slice subdivision basis clue evidence formula guide hand indicant indication indicator indicia model needle pointer rule sign significant symbol symptom token admeasurement admensuration allotment allowance amplification area bang breadth bulk capacity degree depth distance duration fix frequency hit magnitude mass meed mensuration nip pitch quantum ration share shot slug span sum volume weight bite bonus chunk commission corner cut discount duty fee holdout interest juice payoff percent piece of the action points split taste winnings comparison fraction index measure percentage Ratios ratios half cut end bite whole total ratio slice part bit piece atom butt chicken feed chip chunk crumb dab dash division dollop dose dot driblet droplet excerpt flake fraction fragment grain iota item jot lick lump mite modicum moiety molecule morsel niggle parcel particle peanuts pinch portion sample scale scintilla scrap section segment shard share shaving shred sliver smidgen snatch snip snippet specimen speck splinter sprinkling stub stump taste tittle trace trickle board component essential factor fixins ingredient makings part and parcel plug-in principle unit ABCs accessory article brass tacks chapter and verse circumstantiality count cue design dope element fact fine point meat and potatoes minor point minutia nicety nitty-gritty nuts and bolts particular peculiarity plan point respect schedule singularity specialty specification structure technicality thing trait trivia triviality affiliate associate border boundary branch category class compartment degree demarcation department divide dividend divider dividing line divvy grouping head kind lobe member offshoot partition piece of action rake-off ramification sector sort split subdivision wedge ace gob hunk job minim remnant shiver smithereen bisection fifty percent hemisphere constituent detail Fractions fractions eternity space expanse myriad extent vastness beyond ubiquity ending bounds aeon afterlife age ages blue moon dog's age endless time endlessness everlastingness forever and a day future immortality imperishability infiniteness infinitude infinity kingdom come other world perpetuity time without end timelessness wild blue yonder world without end aftertime afterward by and by destiny expectation fate futurity hereafter life to come millennium morrow offing outlook posterity prospect subsequent time to be tomorrow world to come abundance amplitude bigness bulk enormity force high degree hugeness immensity intensity length magnitude mass might potency power prodigiousness sizableness strength aggregation army assemblage assembly collection commonalty concourse congregation crowd crush drove great number heap herd horde host jam legion loads lot lots majority mob much number numbers ocean oodles people plenitude plurality populace proletariat public push quantity scores sea slew swarm throng turnout area arena blank breadth capacity compass distance elbowroom expansion extension field gap headroom headway interval lacuna leeway location margin omission play range reach slot spaciousness sphere spot spread stretch territory tract turf volume zone allotment bit bout chronology clock continuance date day duration epoch era generation hour instance instant juncture lastingness life life span lifetime many a moon moment month occasion pace past point present season second shift span spell stage stint tempo term tide tour turn week while year greatness multitude time Infinity sum total figure count digit emblem prime symbol sign cipher googol folio part one many volume amount lot throng horde crowd slew plenty flock whole lack tally include account run tote reckon tale add come tell add up run to tote up guess bottom line brass tacks certainty clue cue data details dope gospel info inside dope like it is lowdown numbers poop reality scoop score story whole story banking budgeting business commercial economic fiscal monetary numeric pecuniary pocket antecedent argument base bedrock call cause chapter and verse demonstration determinant evidence excuse factor footing foundation goods groundwork inducement information infrastructure justification motive occasion pretext proof rationale reason root seat straight stuff substratum test testimony trial underpinning wherefore why whyfor addition algebra calculation calculus division figures geometry math multiplication subtraction trigonometry bet betting disposition draw drawing flier gambling game of chance gaming long odds lots numbers game pool random shot speculation stake sweep sweepstake tossup wager wagering Bible book canon code commandment decree decretum dictate direction edict law no-nos order ordinance precept prescript principle procedure reg standing order statute facts financial grounds mathematics raffle regulation number Number figure notation symbol cipher numeral integer Arabic chiffer letter sum total count digit emblem prime sign googol folio part one whole number cardinal character decimal denominator fraction numerator ordinal representation statistic number full all gross total every fixed utter uncut choate hurt part broken sick safe mature sound solid good mint complete flawless intact plenary replete thorough together unharmed unhurt unmarred right fit well better hale hearty robust sane strong cured healed unfit weak partial entity jackpot supply being integral summation result fullness quantum oneness unit sum system unity complex lot ensemble body entirety assembly totality coherence lump bulk aggregate linkage amount piece organism quantity sum total the works whole concept one accumulation agglomerate agglomeration assemblage combination conglomerate conglomeration heap mass mixture pile whole ball of wax whole enchilada whole schmear whole shooting match any bar none barring no one each and every entire every bit of every single healthy unimpaired addition bad news budget cost damage expense extent list net outlay output price tag product score set-back tab tidy sum basis bed box chassis core corpus crux essence frame fuselage gist gravamen groundwork hull main part majority material matter pith skeleton staple substance substructure tenor trunk all-inclusive broad-minded charitable comprehensive cosmic cosmopolitan diffuse eclectic ecumenical extensive generic global inclusive indeterminate large-scale liberal open-minded planetary receptive tolerant unbigoted universal unprejudiced unsectarian wide world-wide all right catholic Whole sum total figure count digit emblem prime symbol sign cipher googol folio part one cardinal character chiffer decimal denominator fraction integer numeral numerator ordinal representation statistic whole number number Decimal Decimals funds capital duckets doe moola paper cake cream diniro cheese assets piece of change dollars lump sums digets in lumps firm bent stated rooted pat intent regular fixed settled certain rigid usual agreed weak moving soft located solid situate stiff placed stable strict sited jelled broken fit mien hang air turn port single setting scene scenery flats series array lot batch crowd gang bunch crew circle body bundle outfit band clique mob kit class clan clutch camp sect push clump pack gaggle one head fix lay put apply post wedge point lock affix rest seat plop lodge plant park train stick plank level plunk mount aim cast embed leave move take unfix go up rise end halt name make rate price value allot ruin keep ask jelly clot cake jell gel thin melt drop sink dip grow begin raise abet provoke foment whip up set on stir up cease stop accepted chronic common conventional customary established everyday expected general habitual ordinary orthodox routine set traditional typical accede accept accommodate adapt adjust agree allow approve bow to buy cave in come across come around comply concur conform consent cry uncle cut a deal ditto give in give out go along jibe okay pass play ball reconcile roll over and play dead say uncle shake on submit subscribe yes yield determined hanging tough hard-nosed immovable inexorable inflexible insistent intransigent obdurate relentless resolute set in stone standing pat stubborn unbendable unbending uncompromising unrelenting unshakable unswayable align balance bring into line calibrate connect correct fine-tune focus grind improve improve accommodate mend overhaul polish put in working order readjust rectify regulate renovate repair service sharpen square tighten troubleshoot tune up assert asseverate attest aver avouch avow certify cinch clinch confirm cross heart declare guarantee have a lock on ice insist lock up maintain nail down predicate profess pronounce put on ice ratify repeat rubber-stamp say so state swear swear on bible swear up and down testify vouch witness acknowledge acquiesce admit be of the same mind bury the hatchet buy into check clinch the deal come to terms concede engage give blessing give carte blanche give green light give the go-ahead go along with grant make a deal pass on permit recognize see eye to eye settle side with sign take one up on accustomed adamant affirm sets Set pending ignored tabled settled mutual returned shared answered certain decided requited moot open sure unrequited unreturned betwixt and between changing doubtful faltering hesitant hesitating hot and cold incomplete indecisive irresolute open to question problematical pussyfooting unanswered unconcluded undecided undetermined unfinished unsettled unsolved up in the air vacillating vague waffling unresolved query inquiry inquest poll wringer Q and A answer reply mystery problem debate dispute puzzle protest demur enigma dubiety calm point topic theme subject motion grill search challenge quiz interview seek examine knock hit roast inquire probe pump quest enquire solicit catechize pry petition go over ask about hit up sound out work over find surety oppose suspect hesitate impugn distrust mistrust suspicion impeach believe trust assignment avocation calling case circumstance concern duty employment episode event hap happening incident interest job mission obligation occupation occurrence office function proceeding profession project province pursuit question realm responsibility task thing transaction undertaking address adjuration application bid call claim demand entreaty imploration importunity invocation overture plea prayer proposal proposition recourse requisition solicitation submission suit supplication adjure advance apply ask beg beseech call upon contest crave entreat hit on implore importune plead pray propose refer require resort to strike submit sue supplicate urge agitate canvass clarify expostulate hold maintain reason remonstrate talk about affair beeswax carrying on function goings-on hanky-panky issue lookout matter palaver argue ask advice of be closeted with brainstorm call in cogitate collogue commune compare notes confab confabulate consider deliberate discuss flap groupthink huddle interrogate kick ideas around negotiate parlay pick one's brains powwow put heads together refer to regard respect review seek advice seek opinion of take a meeting take account of take counsel talk over toss ideas around treat turn to appeal business consult Questions Question what why how cheeseburger eating bogan queston funny sarcasm statement interrogative help existence huh? being god question mark commands periods exclamation point confusion math algebra figures numbers decrease reduction general education history language liberal studies literature mathematics philosophy science trivium and quadrivium liberal arts Mathematics analytical scientific measurable numerical algebraic division addition calculus geometry algebra figures numbers decrease reduction algorithmic arithmetical computative geometrical math trigonometric calculation multiplication subtraction trigonometry mathematical mathematics Math easy hard time wasting rape die TED Ted training science study culture learning teaching literacy tutelage guidance breeding finish tuition nurture reading pedagogy tutoring coaching drilling rearing neglect accomplishments acquirement actions atmosphere attainment aura backdrop capacity credentials cultivation deeds education environment framework grounding history practice preparation qualification seasoning tradition upbringing acculturation advancement civility development edification elevation enlightenment illumination polish progress refinement social well-being conduct control curb domestication drill exercise inculcation indoctrination limitation method orderliness regulation restraint self-command self-control self-government self-mastery self-restraint strictness subordination will willpower bodhi broad-mindedness civilization comprehension information insight instruction knowledge open-mindedness sophistication wisdom awareness clarification inspiration perception revelation ability acquaintance apprehension attainments cognition consciousness dirt discernment doctrine dogma dope erudition expertise facts familiarity goods grasp inside story intelligence judgment know-how light lore observation philosophy picture power principles proficiency recognition scholarship schooling scoop substance theory background discipline Education augenblick salon shop den TV room entertaining family room library media room playroom rec room recreation room rumpus room studio exhibit exhibition room hall museum showroom wing apartment attic dormer garret storage flat garden apartment small apartment atelier establishment factory laboratory mill plant foundry works gallery loft studio apartment workshop Studio georg singer leader hazan cantor Cantor
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