quy ước trong toán học_ _ math2it.pdf
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1/15/2015 Quyctrongtonhc?|Math2IT
http://math2it.blogspot.fr/2014/08/quyuoctrongtoanhoc.html 1/10
Math2ITDinh Anh Thi | 15.8.14 | Hiu ton hc | 2Like
Quy c trong ton hc?
Mt bi vit rt hay v vic hiu ng quy c trong ton hc. Quy c l g? C th chng minhc khng? M chng minh c sao li gi l quy c? Cng tm hiu vi tc gi blog Ton hcti p nh.
Trn mt din n n, mt thy gio dy Vt l bo vi mi ngi rng thy y c th chngminh c . Cch chng minh nh sau:
Nh vy c ngha l vic l hon ton chng minh c m khng cn phi quy cnh trong sch gio khoa lp 7. Rt nhiu ngi ng h, h bo rng chng minh n gin md hiu qu. M l chng minh c th cn phi quy c lm g?. Mt vi ngi phn i: l quy c th chng minh lm g? :) Vy l sao, c phi quy c hay khng? M tht ra myci quy c trong ton hc c ngha g, c th quy c khc i c hay khng?
Math2IT: Xin ni trc vi bn c y l nhng kin c nhn v lun bn vton hc ca tc gi bi vit, n khng mang tnh cht l chn l hay mt chngminh ton hc thun ty. Lp lun tuy da trn nhng logic ton hc nhng chmang tnh tham kho dnh cho mi ngi.
TRANG CH LATEX TON LINUX OS X CNTT TRI THC
KHC MATH2IT
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1/15/2015 Quyctrongtonhc?|Math2IT
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u tin cc bn phi hiu l mi chng minh u phi xut pht t nh ngha v cc tin c tha nhn. y ta xem xt ci nh ngha trong sgk nh:
(c tha s a).
nh ngha nh vy l hp l v tch ca n tha s a s l mt s no . nh ngha ny khngth p dng cho trng hp c v tch ca tha s a no c th c ngha l g? Ci trnghp ny r rng l khng c ngha g trong thc t. Tuy nhin do nhu cu pht trin ni ti caton hc ngi ta vn cn xt n . V y l lc cn phi quy c .
Vn l: cng ging nh bao quy c khc trong cuc sng, chng hn thay v ni mt triung ta c th quy c gi l mt chai, hay thay v gi th ny ta c th quy c gi th khc.iu quan trng l ch c quy c c nhn c s ng thun chung ca mi ngi haykhng m thi. l c im quy c trong ngn ng. Vy trn ta c th quy c c khng?
Cu tr li l Khng! Mi quy c trong ton hc u phi ph hp. Chc cc bn u bit tnhcht ny ca ly tha: . Nu m ln hn n, vic rt gn nhng tha s a ging nhau t v mu ta s cn li tch ca tha s , vy nn s bng vi .
Vic quy c s lm cho tnh cht trn vn cn ng trong trng hp . Timun nhn mnh li rng: mi quy c u phi ph hp v ha vo ci chung. Th nn vicchng minh quy c bng cch p dng tnh cht trn ging nh vic tha nhn n ng chng minh n ng vy! C l Thy y ch nn dng nhng phn tch ca mnh ch ra chohc sinh thy s hp l ca vic quy c m thi.
Nu cc bn cn hng th ti xin k tip mt cu chuyn na. C mt hc sinh k rng khi hcv tp hp con, c gio s dnh mt im 10 cho ai chng minh c rng: Tp rng l con cami tp hp. iu th v l trong cc ti liu v tp hp ngi ta u bo rng y ch l quyc! Rt kinh nghim t 1, chc cc bn s ngh rng: i do! l quy c ri cn chngminh ci g na?. Nhng khng hiu sao ln ny ti li mun ng h c gio y: ti ngh khngnh trn l c th chng minh c.
Ta nhc li mt cht v khi nim tp hp con: khi v ch khi
Vy nn chng minh tp rng l con ca mi tp A no ta cn chng minh:
(1)
Mi chuyn th v nm y: tnh ng sai ca mnh ko theo. Mnh ch sai khi ng m li sai thi. iu ny cng c ngha l khi P sai, bn mun suy ra ci g cng c!
Rt ging vi my tnh hung chm gi ca cc bn trai: Em ! Nu anh c nhiu tin th anh sxy cho em 2 ci h bi, mt ci cho em ra mt mt ci cho em ra chn! S thc l bn chngxy cho c y ci g c. D bn ang ngho kit, nhng ch cn ni nu anh c nhiu tin th
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1/15/2015 Quyctrongtonhc?|Math2IT
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noname 5monthsagoTrongtonhcngitakhngaiiquyciucthchngminhc.Vycuhitisaonhtrnthy"chngminh"lhpl,saocnhnkhngdngmiquyc?Phichnghusinhkhy?trliccvnnytixinmnmviyutsau:Luy,utinngitanhngha$a^n=a.a....a$,\foralln\inN=\{1,2,3,...\}$.Sau,dthyctnhcht$a^{m+n}=a^ma^n$,$\frac{a^m}{a^n}=a^{mn},\forallm>n,m,n\inN$.Gingitathyhnhnhctnhchtgchosmm,nghal$a^{n}=\frac{1}{a^n}$,iunycngtngtnh$a^{0n}=\frac{1}{a^n}$.Hay$a^0=1$.Nncuhitralngitasthmmt"tin"lhinnhin$a^{n}=\frac{1}{a^n}$c$a^0=1$hayngcli?Vthitnghkhngpgbngichnthanhnmtthnginnhtmmingithyhplchngminhiuphctphn.cnghpvilogiccaphttrin,khngaiixyciluitottchngminhmtmichicthtrma?Domicvic
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bn mun suy ra ci g m chng c. Th y, ci quy c ca ton hc n nm y: Tonhc quy c rng trong trng hp l Sai, mnh lun lun ng.
Tr li mnh (1) trn, ta thy rng: R rng mnh l sai vi mi phn t ( vrng c phn t no u). Nn mnh ko theo (1) l lun ng ri. iu c ngha l tprng ng l con ca mi tp hp m khng cn phi quy c. Ci quy c tht s y c ll ch quy c v tnh ng sai ca mnh ko theo m thi
2peoplelikethis.Bethefirstofyourfriends.Like
Dinh Anh Thi : Tc gi blog, xut thn l sinh vin s phm ton, hin ang l nghincu sinh v Ton ng dng ti Php. Chnh v nim am m Ton hc, tin hc ng dngv qua trng lp s phm nn Thi rt quan tm n vic ng dng Ton hc, Tin hcvo trong cuc sng thc t cng nh vic truyn t kin thc Ton cho hc sinh theomt phung php hin i v tch cc nht, gy hng th v hiu su cho ngi hc,ngi c ni chung. Mi chi tit xin lin h [email protected]. Blog c nhnAnh Thi blog.
4 X 4
15.8.14 Hiu ton hc
Vit bi cng blog bng cch lin h [email protected].
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1/15/2015 Quyctrongtonhc?|Math2IT
http://math2it.blogspot.fr/2014/08/quyuoctrongtoanhoc.html 4/10
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khngaiixyciluitottchngminhmtmichicthtrma?Domicviclachn$a^0=1$sauxydngvmrngcutrciscaphptnhlythasangchosm.Tmli,ccbiuthcmccbngilchngminhcho$a^0=1$trnchlingcliviconngcaphttrincaphptnhlytha.Trongkhingitathanhniunhb$a^0=1$,maicngcththynhpl,xydngphplythachosm.Chcccbnhctt.
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inhAnhThi 5monthsagoMod >nonamebnning,cicchchngminhgingnhkiulycub)chngminhcua)trong1cuhivy.Tuynhinnhtcgibivitcp,quyctuyddngnhngphiphhpvilogictonhc,cthlcucngcngiquyca^0=2hongchng,nhngquaqutrnhsuylunlogicvthcttonhc,cibloitr.Vilia^0=1kophiaicngcththylnngu,bnthhihsbygivnhngngikochuyntonxemhbittisaohem,tinchmangtml"chpnhn"lchnhthi:)
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noname 5monthsago>inhAnhThiNhni,bnthna^0=1lchpnhn.tmrngphptnhlythavncnngchosmm.Dohcsinhchpnhna^0=1lhinnhinm?
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inhAnhThi 5monthsagoMod >nonamehinnhinvingithythi,cnhcsinhthchngchpnhntheokiuvt,mnhnilth.nhiukhimnhdychnga^0=2chngcngkonig,trnhngacbitrc,nhngathngminh.
PS.saukhickcommentcabn,mnhhiuthmcabnri,chcbncngchahiumnh,mnhkonila^0cthchngminhc,mnchmangtnhhpltonhcmthi.ivinhngngitipxcton,c2kiuchpnhn,1lchpnhnkiuvt,2lchpnhndicchhiucalogictonhc.
noname 5monthsago>inhAnhThiKohpllm:Nhvi5tinclic,chngtachpnhnn,xydngnnhnhhcclic.Gibo2ngthngsongsongkoctnhauclogicko,haychpnhnvt?th...khmnic.Nunhdngnhngtnhchthnhhcbnbitsauny,nilnlogic,thelhikhngcngbng,binhngcisaunylcsinhratmcan,nhngtincchpnhntrc.rimicchuynmtanhchngkhckinquytkochuchpnhntinsongsong,ngtaningclinctnhau,nunilogicthtathyisaomlonydhmth,haingsongsongrinhaurrngkoctnhaumhnboctnhiulngkhc,cuicnglisinhrahnh
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1/15/2015 Quyctrongtonhc?|Math2IT
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koctnhaumhnboctnhiulngkhc,cuicnglisinhrahnhhcPhiclicmnhtnhngdngcanliykhoahcconngirangoikhnggian?
Vyclchpnhnvthaykhngvtliukhmlunbn,tanhnvothyncvhpl(kocnghallogic)tachpnhnnhnngxydngnnnhngcngtrnhkhcbngccphpsuylunlogic.Doniashcsinhchpnhnvttherngnhnxtcphntiucc.:D
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inhAnhThi 5monthsagoMod >nonameHnhnhchngtaangivotranhcicphnvlthphi.Trckhitrlitipxinhibnclgiovinkhngvy?Tichngigiovinmibitlhcsinhchpnhnvtlnhthno.Mnhnithkhichngtadychohctr,cgng(mnhchnicgng)llmsaochochnghiubnchtvntrong1chngmcno.Vaphnkinthctonngynaydychohctrkophivtlg?Chngbaogicngcanhcnhtrongu1cuhi"hcchi?hcthi?"Ci"tiucc"bnnikodnhchohsmdnhchosgiodchs,dnhchochngtachngtartkinhnghim.
BnvdvtinphiEuclidelngnhngnhmnhni,chngtacquyngis,cquyn"chpnhnvtiv"nhbnni,ok,nutcha^0=2mbncthra1ngnhmi(gidnh"philytha"hayg)mnctnhllunthctinthvnok.Cimnhnillogictrongnhnggcphthinvconngichpnhntingyhmnay.
Xinnhcli,bnthntonhckophilthconngitora(tchngta"chpnhn"tchngtachonlphilcnocngclsai)mngnglinvinhucuvthctin.:D
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noname 5monthsago>inhAnhThiPhichngbnanglycingcphasauangcnicitrcmtchngtamic?Xinhillythasm,lcictrclytha0,haythanhnmtcchhpllytha0mrngralythasm?,Nulmrcvn,tashiuciumnhangniylg.Mnhkonibthcsinhchpnhnmith,nhnglgiovincngnnhiutrnhtcakinthchcsinhchc.Nghalchabitnhngcisaulghtro,conngitamimmmi,nhngha,riphttrinnramtcchtnhin.Donuko"vt"chpnhna^0=1thccmycisaunychochngtahcko?Vybnchorngttincng"vt"ccthngyhmnay?
inhAnhThi 5monthsagoMod >noname
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1/15/2015 Quyctrongtonhc?|Math2IT
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Bi ng C hn
CchtofilevnbnbngLaTeX21comments5monthsago
haduyanhCmnbnnh.Mnhsacri
Ngnkhngchocopytextbivittrongblogger5comments6monthsago
holalatigeranhichoemhicinotevngvngtrongbivitmnhdngwidgetghayththutglmcvyanh,em
ThmhthngcommentDisQusvoblogger13comments6monthsago
inhAnhThia,mnhvnthynhcabnm?Khkhncabnlg,bnnirhnckhng?
SonthotonhctrongLaTeX(k1)4comments5monthsago
thuthaoNguyenlnThi^^
ALSOONMATH2IT
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Rrngmnhngvibnngitacnbitcilythamlgnnngitaminhnghalytha0trc.
Vhshcdatrnnhnglthuytcchngminhlngnntinantmthahm"vt".Chkutonhcbnthnnvtmracimithcoichngkon.Vtphivttheokiunona,vttheokiuEuclideldatrnciclcatnhin.Chkophivttheokiu"i,bitonnykhqu,tavticigithitnyirichngminhtip",saingaycigcthlmsaongktquc?
Ttincngvtsainhiulmchkophitu,maymnthaysaunyngitakpphthin.
Cngnhmnh(dnton)anghcgiitchs,cnglptrnhmphng1hintngcatnhin.Titinhccnglptrnhnhvy.Tinra1biu,mnhcngrabiu.Cikhccbnca2bnchnhltinkoclluntonhcchngminhccphngtrnhvmhnhcatinlng.Rtnhiubibokhoahccng"gis"choranhiuktqunhngsaunyhcngphthinracigischathtsng.Thmchhctnhgiskothctgiinhngbitonngintrcdbitrngnsai.vttheokiucatitinthnguyhimlm,sai1lii1dm.
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1/15/2015 Quyctrongtonhc?|Math2IT
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Tuyn tp cc eBooks hiu thmv th gii ton hc k th (cp
nht ngy 10/12/2014)
Tnh hp l ca nghim hphung trnh v khi nim
'condition number' ca mt ma trn (k1)
vui: Anh chng chy xe (pn)
Cc website hay dnh cho vichiu ngha thc tin ca ton
hc (update 12/9/2014)
Hiu v khi nim 'gii hn' trongton hc (k 2)
Bi lin quan
Gii thiu
Math2IT l chuyn trang v Ton hc+ Gio dc v Cng ngh. Mongmun chia s tri thc v kht khao imi nn gio dc nc nh. cthm.
Theo di chng ti
+38 xut url ny trn Google
Nhiu nht 7 ngy qua
Nhng cch v hnh chnh xc bng
Math2ITTon&Tin1,461Like
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1/15/2015 Quyctrongtonhc?|Math2IT
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thc k v compa
Nhng vic cn lm sau khi ciUbuntu 14.04 v mt s phin
bn khc
Nhng phn mm nn ci choUbuntu, Elementary OS, Linux
Son tho ton hc trong LaTeX(k 1)
WolframAlpha : gii ton theotng bc
Tng hp nhng vic cn lmsau khi ci Windows c mt
chic my tnh y mnh m
Ti liu tham kho dnh cho itng t hc LaTeX (cp nht
ngy 6/11/14)
Bi ngu nhin
Nhng bi vit ang trong giaion hon tt
[TeXTips] Thm t kha gi lcg trong TeXMaker
Nhng li LaTeX thng gpnht
vui: Anh chng chy xe (pn)
Chuyn file hnh trong Matlabsang code hnh v trong LaTeX
Nhiu nht 30 ngy qua
Nhng cch v hnh chnh xcbng thc k v compa
Nhng vic cn lm sau khi ciUbuntu 14.04 v mt s phin
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1/15/2015 Quyctrongtonhc?|Math2IT
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bn khc
Nhng phn mm nn ci choUbuntu, Elementary OS, Linux
Ti liu tham kho dnh cho itng t hc LaTeX (cp nht
ngy 6/11/14)
Son tho ton hc trong LaTeX(k 1)
WolframAlpha : gii ton theotng bc
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bn c th cho mnh xin link face cabn.. mnh c th trao i trc tip vibn.. bn gip...
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a, mnh thy n khi n lch th mi pm bn, khi y th cc bi n "kht" lic vi nhau...
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