Upload
pham-thi-thanh-thuy
View
15
Download
0
Embed Size (px)
Citation preview
1/15/2015 Hiumtsdngvnhtrongtonhck1:1/0v0^0|Math2IT
http://math2it.blogspot.fr/2014/08/hieumotsodangvoinhtrongtoanhoc.html 1/9
Math2IT
Dinh Anh Thi | 16.8.14 | Hiu ton hc | Ton s cp | 6Like
Hiu mt s dng v nh trong ton hc - k 1: 1/0v 0^0
Bi vit c gng tm hiu ti sao li c nhng dng v nh nh 1 chia 0, 1 m v cng, 0 nhn vcng, ...
Ti sao 1/0 khng c ngha?Bi v php chia c nh ngha da trn php nhn. Bn khng th no tm c mt gi trthch hp sao cho nhn vi gi tr bng 1 v 0 nhn vi bt k s no u bng 0. Do khng c ngha .
Ti sao v nh?Chng ta bit mi s m 0 u bng 1, 0 m bt k s no u bng 0. Cu hi t ra l khi y bng bao nhiu?
Tht ra cu tr li l "khng xc nh". S d nh vy v hm s theo hai bin l mt hms khng lin tc ti gc ta . Ngoi ra bn c th d dng bin i v dng (cng lmt dng v nh quen thuc, bn vui lng theo di cc k tip theo ca lot bi) bng cch
4
5
4 5
g
MO g MO g
TRANG CH LATEX TON LINUX OS X CNTT TRI THC KHC MATH2IT tm
1/15/2015 Hiumtsdngvnhtrongtonhck1:1/0v0^0|Math2IT
http://math2it.blogspot.fr/2014/08/hieumotsodangvoinhtrongtoanhoc.html 2/9
Cu tr li c gi l 1 v sau y ta s tip cn mt s cch lp lun ti sao li nh vy :
H s hng th ca tam gic Pascal trong khai trin nh thc cho ta kt quca . Tt cc h s cc hng ngoi tr hng trn cng u l v . Tuynhin h s hng trn cng (tng ng vi ) trong tam gic Pascal lun l 1. Do ,nu c th nh ngha c, th ta s c .Gii hn ca khi (t pha bn phi) lun l . Bn c th xem chng minh iuny Ph lc.Biu thc c ngha rng bn s nhn vi chnh n ng ln. Do , ging nhmt "tch rng", v n s bng 1 bt k m bng bao nhiu v bt u mt tch no y ta uc mt s 1 n mnh trong .Mt cch khc hiu v biu thc l s cch tng ng (map) mt tp hp -phnt sang mt tp hp -phn t. R rng KHNG c cch no map mt tp hp gm 2-phn t sang mt tp rng, tng ng . Nhng nu ta mun map mt tp hp rngvo chnh n th ta c th dng nh x ng nht, hay khi ta c th thy . XemPh lc hiu r hn v tng map t tp ny sang tp kia.
Nhng iu trn ch l "pht ni hng" lun bn thm v dng v nh m thi, ta tha bitkt qu chc chn rng l khng th xc nh nn n khng th bng 1 hay bt c gi tr nokhc c.
Ph lc
Cu hi t ra, nu (ch l nu) ta c th nh ngha c th ta s gn gi trcho n l 1 hay l 0 y?
*
*
*
'
'
*
4
4
4
)
*
) * )
)
*
*
)
Chng minh . MJN4
4
4
MO
4
1/15/2015 Hiumtsdngvnhtrongtonhck1:1/0v0^0|Math2IT
http://math2it.blogspot.fr/2014/08/hieumotsodangvoinhtrongtoanhoc.html 3/9
Gi s tp c phn t, tp c phn t. bi c th hiu l ta mun tm tt c cc"hm s" c tp ngun (domain) l v tp ch (range) l . Cn nhc li rng mt hm s it n l mt nh x i t vo trong tha mn 2 iu kin sau:
Tp ngun ca l .Mi phn t trong , c duy nht mt nh thuc . Nu v th
.
V d, nu v th
Vi phn t , c 3 cch chn cc phn t nm trong .Tng ng vi mi cch chn phn t , ta c thm 3 cch chn cho phn t .
Nh vy ta s c tng cng cch chn hm s t vo . Minh ha nh bn di
(
Ti liu tham kho[1] Su, Francis E., et al. Zero to the Zero Power. Mudd Math Fun Facts.[2] Dr. Math, Why are Operations of Zero so Strange?. Math Forum.[3] Wikipedia, Quy tc L'Hospital .
MJN
4
4
4
MJN
4
!
MO
4
4
MJN
4
!
4MO4
!
4MO4
MJN
4
!
MJN
4
MO4
4
!
MJN
4
MO4
4
QEOHRVZUD-)PTQJUBM
!
MJN
4
4
4
!
xnh x t tp sang tp )*
* )
"
"
4 5 4 5 " 4 6 "
5 6
\ ^ \ ^
g
"
"
\ ^
1/15/2015 Hiumtsdngvnhtrongtonhck1:1/0v0^0|Math2IT
http://math2it.blogspot.fr/2014/08/hieumotsodangvoinhtrongtoanhoc.html 4/9
6peoplelikethis.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.
16.8.14 , Hiu ton hc Ton s cp
Vit bi cng blog bng cch lin h [email protected].
1/15/2015 Hiumtsdngvnhtrongtonhck1:1/0v0^0|Math2IT
http://math2it.blogspot.fr/2014/08/hieumotsodangvoinhtrongtoanhoc.html 5/9
Tuyn tp cc eBooks hiu thmv th gii ton hc k th (cp
nht ngy 10/12/2014)
Hi p Ton (my tnh cm tay) -
Bi lin quan
Bi ng C hn
NhngviccnlmsaukhiciUbuntu14.04vmtsphinbnkhc4comments6monthsago
hongdiepCmnbnrtnhiu,mnhlmtheocchcabn,mcdbbolinhngvnvocphnvngntfs(tr
HipLaTeX(k1)3comments6daysago
BiSangThMonglmanhhngdntntnhgiovintonchngticthtocmtblogchuynnghipnhcaanh.
Tont'Lnutrang'(Backtotop)cunmtchoBlogger1comment6monthsago
VietOverlandTravelCmnbnnh.Itworksperfectly:)!!!Vietnamoverlandtours
Quyctrongtonhc?8comments5monthsago
nonameTrongtonhcngitakhngaiiquyciucthchngminhc.Vycuhitisaonhtrnthy"chngminh"
ALSOONMATH2IT
0Comments Math2IT Login
SortbyBest Share
Startthediscussion
Bethefirsttocomment.
WHAT'STHIS?
Subscribe AddDisqustoyoursited Privacy
Favorite
Bi ng Mi hn
1/15/2015 Hiumtsdngvnhtrongtonhck1:1/0v0^0|Math2IT
http://math2it.blogspot.fr/2014/08/hieumotsodangvoinhtrongtoanhoc.html 6/9
k 1 : tm hai s nguyn dng tho iukin
Gii ton theo tng bc vitrang web CyMath.Com v
Symbolab.Com
Tuyn tp thi v p n ihc mn Ton Khi A t 2002
n 2014
Tuyn tp thi i hc mnTon t 2002 n 2012 theo ch
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 xcbng 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)
Math2ITTon&Tin1,461Like
1/15/2015 Hiumtsdngvnhtrongtonhck1:1/0v0^0|Math2IT
http://math2it.blogspot.fr/2014/08/hieumotsodangvoinhtrongtoanhoc.html 7/9
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
Cch ci v s dng Homebrewv MacPorts trong Mac OS X
Tm hiu v Memory Compresstrong Mac OSX
Kinh nghim to mt blogchuyn nghip vi blogger
Tuyn tp cc eBooks hiu thmv th gii ton hc k th (cpnht ngy 10/12/2014)
B mt sau nhng sut n trnmy bay
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
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)
1/15/2015 Hiumtsdngvnhtrongtonhck1:1/0v0^0|Math2IT
http://math2it.blogspot.fr/2014/08/hieumotsodangvoinhtrongtoanhoc.html 8/9
WolframAlpha : gii ton theotng bc
Google+
Math2IT
+ 38
Theo di
Lt xem
111191
Nhn xt mi
Ti liu min ph
bn c th cho mnh xin link face cabn.. mnh c th trao i trc tip vibn.. bn gip...
To phn trang c nh s cho blogger 2 hours ago
inh Anh Thi
a, mnh thy n khi n lch th mi pm bn, khi y th cc bi n "kht" lic vi nhau...
To phn trang c nh s cho blogger 3 hours ago
Ti liu min ph
Bn inh Anh Thi cho mnh hi thm ciny na nh !! hjhj trn trang ch blogbi ng n c b...
To phn trang c nh s cho blogger 12 hours
ago
inh Anh Thi
Hix, mnh cng nh mua n bn, mnhkhng r bn i, thng th bn nn hicng ty bn tn min...
1/15/2015 Hiumtsdngvnhtrongtonhck1:1/0v0^0|Math2IT
http://math2it.blogspot.fr/2014/08/hieumotsodangvoinhtrongtoanhoc.html 9/9
ANDROID BLOGGER-BLOGSPOT CHUYN TON HC
EBOOK GAME GIO DC HIU TON HC
HI P HI P LATEX HI P TIN
HI P TON KHC KHM PH
KIN THC CNG NGH KIN THC THPT LATEX
LINKS LINUX LI LATEX MATH2IT OSX
PHN MM TEX CHUYN NGNH TEXTIPS
TH THUT IT TON TON CAO CP TON S CP
TI SAO T HC LATEX THI VUI
To phn trang c nh s cho blogger 1 day ago
Theo di qua email
Emailcabn... SUBMIT
Chuyn mc
2012 Math2IT | Thit k bi Template Trackers | Chnh sa bi inh Anh Thi