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Язык математической разметки MathML

Язык: русский
Формат: курсова
Тип документа: Word Doc
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sscue ?aciaoee iaoaiaoe/aneeo aeieoiaioia.

Iaoaiaoe/aneee ycue Markup (MathMl) yaeyaony XML i?eeeaaeiie
i?ia?aiiie, iic

aieythuae iienuaaoue iaoaiaoe/aneea no?oeoo?u e au?aaeaiey. Oeaeue
MathMl ninoieo

a oii, /oiau aeaoue aiciiaeiinoue inouanoaeyoue niaoeeoe/aneea
iaoaiaoe/aneea i?iae

ou a Web-naoe.

1. Aaaaeaiea

1.1 Iaoaiaoe/aneea eaeae e eo caienue.

Ioee/ea iaoaiaoeee io ae?oaeo iaoe ninoieo a eniieueciaaiee eiiieaena
auniei

?acaeoie nenoaiu neiaiee/aneeo caienae. Iaoaiaoe/aneea eaeae e caiene,
n ii

iiuueth eioi?uo iie eceaaathony, nouanoaotho iacaaeneii ae?oa io
ae?oaa. Aeaenoaeoaeue

ii, iiiaea iieiaeaiey yeaiaioa?iie iaoaiaoeee iiaeii caienaoue,
eniieuecoy iau/iua

neiaa. Iaeiaei oiaiea i?aaenoaaeyoue eaeae a neiaieueiie oi?ia
yaeyaony iniiaiui

i?e aiaeeca e iia?e?iaaiee aeaiiuie a iaoaiaoeea.

A iaoaiaoeea niaeaoaiey i oi?ia caienae iinyo eiiieaeniue oa?aeoa?.
A?eoiaoe

/aneea au?aaeaiey, iai?eia?, caienuaathony n eniieueciaaieai oeeo?,
ia?aiaiiuo e

noaiaea?oiiai iaai?a ciaeia aeey iaicia/aiey a?eoiaoe/aneeo iia?aoeee.

Oai ia iaiaa o?oaeiinoe aicieeatho i?e iiiuoeao iaea/ue a
ienueiaiioth oi?io aea

aea iaeaieaa i?inoua ec iaoaiaoe/aneeo au?aaeaiee. Ionthaea neaaeoao
iaiaoiaeeiinoue

nicaeaiey nenoaiu neiaieueiuo caienae, eioi?ay iiaea au
eniieueciaaoueny ai anai

ie?a.

A ?acaeoea oi?i iaoaiaoe/aneie caiene nouanoaaiiue aeeaae aianea
oaoiieiaey

nayce.A naiai ?acaeoee iia i?ioea iooue io aeeiyiuo ieaioaoia e
iaie?onia aei

ia/aoiiai niiniaa i?aaenoaaeaiey eioi?iaoeee, a iaoaiaoe/aneea caiene
aaeenue n

eniieueciaaieai aiciiaeiinoae, i?aaeinoaaeyaiuo oaoiieiaeae nayce ia
?acee/iuo

a?aiaiiuo yoaiao.

A ianoiyuaa a?aiy aicieeea iiaay n?aaea nayce, i?aaenoaaeaiiay YAI n
naoaaie

no?oeoo?ie. Yoi ioe?uaaao iiaua aiciiaeiinoe aeey ia?aaea/e e
i?aaenoaaeaiey iaoa

iaoe/aneie eioi?iaoeee.

1.2 Oeaee i?iaeoa

1.2.1 I?aaeiinueee nicaeaiey MathMl

Ia?aiia/aeueii WWW i?aaeiacia/aeanue aeey o/aiuo. Ii a oiaea
eniieueciaaiey WWW

auynieeinue, /oi eioi?iaoeey, ia?aaeaaaaiay ii aa eaiaeai,
i?aaenoaaeyao eioa?an

ia oieueei aeey niaoeeaeenoia. Ii aiciiaeiinoe aeeth/aiey
iaoaiaoe/aneeo au?aaeaiee

a HTML ieacaeenue i/aiue ia?aie/aiiuie. Noaouee caienuaaeenue a
caeiaee?iaaiiie

oi?ia, iniiao eioi?ie ninoaaeyee iaai?u neiaieia ASCII.

Naaiaeiy HTML iicaieyao ia?aaeaaaoue iaoaiaoe/aneea niiauaiey,
iaeiaei iaoaieciu

eo nicaeaiey e iineaaeothuae ia?aaioee ianoieueei neiaeiu, /oi iiiuoee
iieueciaaoa

eae aeeth/eoue a niiauaiea aeaaea naiua i?inoua oi?ioeu caeai/eaathony
iaoaea/ae.

Ianiio?y ia oe?ieia ?ani?ino?aiaiea Web, iaaeinoaoie iiaeaea?aeee
iao/iie nayce

ia?aie/eaaao noa?o aa i?eiaiaiey.

1.2.2

I?iaeaiu, aicieeathuea i?e caiene iaoaiaoe/aneeo au?aaeaiee, iiaeii
?acaeaeeoue

ia aeaa a?oiiu : i?iaeaiu eiaee?iaaiey e i?iaeaiu ?aaeecaoeee.
I?iaeaiu, naycaiiua

n aeeth/aieai a aeieoiaio iaoaiaoe/aneeo caienae eae
eeethno?aoeeiiiiai iaoa?ea

ea, ioiinyony e i?iaeaiai ?aaeecaoeee.

A iineaaeiaa a?aiy ia?ainoaiaiioth aaaeiinoue i?eia?aoatho ?acee/iua
niiniau aa

oiiaoe/aneie ia?aaioee aeaiiuo.

Iiyoiio ?aoaiea i?iaeaiu eiaee?iaaiey iaoaiaoe/aneeo caienae aeey Web
aaaeiaa,

/ai ?ac?aoaiea i?iaeaiu ?aaeecaoeee, ii e aa iaeuecy eaii?e?iaaoue.

1.2.3 Oeaee i?iaeoa MathML

Oeaeue i?iaeoa ninoieo a ?ac?aaioea i?eeeaaeiuo i?ia?aii,
iiaeoiaeyueo eae aeey iao

/aiey, oae e aeey iiaeaea?aeee iao/iie nayce, n /ueae iiiiuueth iiaeii
?aaioaoue n iao?e

oeaie, iineaaeiaaoaeueiinoyie e ?yaeaie, inouanoaeyoue ?aaeaeoe?iaaiea
iaoaiaoe/an

eeo au?aaeaiee. I?aaeoniao?eaaaony iiaeaea?aeea i?iniio?a aeeeiiuo
au?aaeaiee, i?aaein

oaaeaiea aiciiaeiinoae eniieueciaaiey iae?ieiiaiae, iiauo noai
eniieiaiey, iiauo

neiaieia.

1.2.4 Oeaee ?aaeecaoeee

Eoae, oeaeue i?iaeoa MathML – ?ac?aoaiea i?iaeaiu eiaee?iaaiey
iaoaiaoe/aneie

eioi?iaoeee.

Oeaee ?aaeecaoeee – yoi e?aoeia iienaiea ooieoeeiiaeueiuo
aiciiaeiinoae MathML.

* Ia/aoue MathML o?aaiaiee aeieaeia inouanoaeyoueny ia i?eioa?ao n
aunieie

?ac?aoathuae niiniaiinoueth.

* I?e ?aaioa n iaoaiaoe/aneeie caienyie aiciiaeii eniieueciaaiea
iuoe.

* Naycue MathML caienae n i?eeeaaeiuie i?ia?aiiaie inouanoaeyaony
/a?ac ieii

i?iniio?a.

Inouanoaeaiea oeaeae ?aaeecaoeee iiaeao iaania/eoue ?anoe?aiea
iaeanoe eniieue

ciaaiey HTML aeieoiaioia. Iieueciaaoaee iieo/ao aiciiaeiinoue
i?iniao?eaaoue eo a

eioa?aeoeaiii ?aaeeia, aeaeaoue ?ania/aoee e i?.

Iaeiaei aeey iaeaieaa iieiie ?aaeecaoeee aiciiaeiinoae yeaeo?iiiuo
aeieoiaioia

iaiaoiaeeii iaania/eoue acaeiiaeaenoaea iaaeaeo ieie e HTML
iaoaiaoe/aneeie aeieo

iaioaie.

1.3 I?eia?u i?eiaiaiey iaoaiaoe/aneeo no?oeoo? ia Web

Ni?in ia yooaeoeaiua n?aaenoaa yeaeo?iiiie iao/iie nayce aunie.
Eiee/anoai eth

aeae, iieuecothueony oneoaaie yeaeo?iiiie nayce, iinoiyiii ?anoao.

1.3.1 Ia?aciaaiea

A ianoiyuaa a?aiy eaeao aeoeaiue i?ioeann aeeth/aiey eioa?aeoeaiuo
iaoa?eaeia

a o/aaioth i?ia?aiio. Iaeiaei no?iaea a?aiaiiua e oaoie/aneea
ia?aie/aiey nicaeatho

o?oaeiinoe i?e eniieueciaaiee eioa?aeoeaiuo iaoa?eaeia ia caiyoeyo ii
iaoaiaoe

/aneei aeenoeeieeiai.

Iai?eia?, inouanoaeoue i?iaa?eo yecaiaiaoeeiiiuo ioaaoia ia IE
iaaiciiaeii aac

oiaiey caienuaaoue iaoaiaoe/aneea au?aaeaiey ia ycuea, iiiyoiii
iaoeia. Neaaeothuei

oaaii eniieueciaaiey iiauo oaoiieiaee a iaeanoe ia?aciaaiey yaeyaony
nicaeaiea

eioa?aeoeaiuo o/aaieeia.

1.3.2 Iao/iua enneaaeiaaiey

Ia naaiaeiyoiee aeaiue nouanoaoao ieiei aethaeeiu yeaeo?iiiuo
iaoaiaoe/aneeo ecaea

iee. A ieo niaea?aeeony aieueoia eiee/anoai iaoaiaoe/aneeo caienae,
auiieiaiiuo ia

TeX.

Nouanoaoao aa?ney “oeie/aneiai” markup ycuea – CML, iniiaie eioi?iai
oaeaea

yaeyaony XML.

1.3.3

Neaaeothuay i?iaeaia yeaeo?iiiie nayce e niioonoaothueo ae
i?eeiaeaiee – ianiaian

oeiinoue ?acee/iuo nenoai. Iai?eia?, noaouee, auiieiaiiua a Tex,
ianiaianoeiu ni

noaoueyie, iaa?aiiuie a Word. ?acoeueoaoaie iiaeiaiie ianiaianoeiinoe
yaeythony o?oae

iinoe a ia?aaea/a e eniieueciaaiee eioi?iaoeee.

1.3.4 Ioaeeeaoeee

Aei iaaeaaiaai a?aiaie yeaeo?iiiua aeo?iaeu ia iieueciaaeenue
iiioey?iinoueth ec-ca

oeacaiiuo auoa i?e/ei, iaeiaei n ?acaeoeai markup ycueia neooaoeey
ia/eiaao ia

iyoueny.

1.4 Web e iaoaiaoe/aneee markup ycue

Iaoaiaoe/aneea caiene aieaa, /ai oaeno, o?oaeiu aeey ia?aaioee. Ii,
iie?aynue ia no

uanoaothuea markup noaiu e ooieoeeiiaeueiua aiciiaeiinoe HTML, MathML
iaania/eaaao

iiaeaea?aeeo nayce i?e ?aaioa n iaoaiaoe/aneeie iauaeoaie ia Web.

1.4.1 Naycue MathML c ae?oaeie iaoaiaoe/aneeie markup ycueaie

TeX yaeyaony iaeiei ec iaeaieaa aeeyoaeueiuo iaoaiaoe/aneeo markup
ycueia 2-o

iineaaeieo aeanyoeeaoee.

TeX ,aac niiiaiey, ieacae nouanoaaiiia aeeyiea ia MathML. Iaeiaei
anoue ianeieueei

aniaeoia, eioi?ua ia iicaieytho eniieueciaaoue TeX aeey ?aaiou a Web.

Oai ia iaiaa,TeX onoaiiaee noaiaea?ou ea/anoaa aecoaeueiiai
eniieiaiey, eioi?ui

niioaaonoaoao MathML.

Aoi?ui markup ycueii, ieacaaoei nouanoaaiiia aeeyiea ia ?acaeoea
MathML, yaey

aony ISO 12083.

A iniiaa ISO 12083 eaaeeo TeX, /oi icia/aao iaee/ea o ISO 12083
iaaeinoaoeia

Tex, iaeiaei ISO 12083 aieaa iiaeoiaeeo aeey aaoiiaoe/aneie ia?aaioee
aeaiiuo.

1.4.2 XML

A aeiiieiaiea e auoaneacaiiiio, MathML aeieaeai niaeaniauaaoueny e n
nouanoaoth

uae HTML n?aaeie.

Iaeiei ec niiniaia niaeaniaaiey yaeyaony ?acaeoea XML – oi?iuaiiiai
aa?eaioa

SGML, ?ac?aaioaiiiai aeey Web. XML iicaieyao aaiaeeoue e
eniieueciaaoue iiaua ioiao

ee. A oi aea a?aiy XML neioaenen ouaoaeueii ii?aaeaeyao no?oeoo?o
aeieoiaioa, /oi

iaeaa/aao aaoiiaoe/aneoth ia?aaioeo e nii?iaiaeaeaiea aieueoeo
ianneaia aeaiiuo.

XML iiaeoiaeeo aeey ?aciaoee neiaeiuo e niaoeeaeece?iaaiiuo aeaiiuo.
A neeo auoanea

caiiiai MathML iiaeii ii?aaeaeeoue eae XML i?eeeaaeioth i?ia?aiio.

1.4.3 ?aaeecaoeey

XML i?aaeinoaaeyao niinia ii?aaeaeaiey no?oeoo?u e neioaenena.
Iaoaieciu ia?a

aioee e i?aaenoaaeaiey eioi?iaoeee MathML o?aaotho aeaoaeueiie
?ac?aaioee.

Aeey ia?aaioee aeaiiuo MathML iaiaoiaeeii ?anoe?eoue aiciiaeiinoe
ieii i?iniio?a.

1.5 Iauea i?eioeeiu MathML

1.5.1 Eiaee?iaaiea eioi?iaoeee

Nouanoaoao aeoaieay naycue iaaeaeo iaoaiaoe/aneeie eaeayie e eo
caienueth.

Iaoaiaoe/aneay caienue, auiieiaiiay n niaethaeaieai i?aaee,
eneeth/aao aeaiyeia oie

eiaaiea.

A iaeioi?uo neo/ayo neiaiee/aneay e iaoaiaoe/aneay no?oeoo?a caiene
yeaeaa

eaioiu. A iiaeiaiuo neooaoeeyo MathML i?aaeeaaaao eniieueciaaoue
ioiaoee oeia

, e .

?anniio?ei i?eia? : .Eniieuecoy ioiaoee MathML, aai
iiaeii caie

naoue oae :

(

x

+

2

)

2

A aeiiieiaiea e ioiaoeai i?aaenoaaeaiey MathML niaea?aeeo aua
i?eia?ii 50 ?acee/

iuo ioiaoie. Eniieuecoy yoe ioiaoee, i?aaeuaeouee i?eia? iiaeii
caeiaee?iaaoue oae:

x

2

2

1.5.2

Aeey oaaee/aiey iieueciaaoaeueneie aoaeeoi?ee iaiaoiaeeii ?anoe?aiea
aiciiaeiinoae

MathML. E iei ioiinyony e caaea/e ii oniaa?oainoaiaaieth iaoaiecia
eioa?oaena.

2. Iniiau i?aeoe/aneiai eniieueciaaiey MathML

A yoii ?acaeaea i?aaenoaaeai e?aoeee iaci? i?eioeeiia ?aaiou MathML.

2.1 Eniieueciaaiea ioiaoie i?aaenoaaeaiey MathML

Ioiaoee i?aaenoaaeaiey MathML eniieuecothony aeey iienaiey no?oeoo?u
iaoaiaoe/an

eie caiene. ?anniio?ei i?eia? :

x

2

+

4

⁢

x

+

4

=

0

Caeanue noieo ia?aoeoue aieiaiea ia aeaa aniaeoa: ai-ia?auo, a
i?eia?a i?enoonoao

tho ioiaoee oeia MI,MN,MO e “aeiaeaiiua” ioiaoee oeia MSUP e MROW, a
ai-aoi?uo,

ioiaoee oeia MROW eniieuecothony aeey iaicia/aiey oneiaey, a aeaiiii
neo/aa i?aaen

oaaeaiiiai iia?aiaeii “=”.

Ioiaoee, niaea?aeauea aeaiiua, oeacuaatho ia eo oei. Iai?eia?,
ioiaoea MI oeacuaaao

ia eaeaioeoeeaoi? eee ia?aiaiioth, a ioiaoea MN – ia iiia?. Ae?oaea
ioiaoee iaic

ia/atho noaio ?aciauaiey. Eaaeaeay noaia ?aciauaiey niaea?aeeo
ii?aaeaeaiiia /enei

iiaeau?aaeaiee a noi?iaii ii?yaeea. Iai?eia?,MSUP noaia aeieaeia
niaea?aeaoue a oi/

iinoe aeaa iiaeau?aaeaiey.

x

=

b

&PlusMinus

b

2

4

⁢

a

⁢

c

2

⁢

a

A yoii i?eia?a neaaeoao ia?aoeoue aieiaiea ia oi, /oi ciae
“iethn/ieion” – nia

oeeaeueiue iieiaiiaaiiue iauaeo. MathML i?aaeinoaaeyao aieueoie nienie
eiai iaoa

iaoe/aneeo iauaeoia.

A

=

[

x

y

z

w

]

2.2 Eniieueciaaiea MathML niaeaniuo ioiaoie

x

2

4

x

4

0

Ioiaoee EXPR eniieuecothony a oii neo/aa, eiaaea niaea?aeaiea iineo
iaoaiaoe/aneee

oa?aeoa?.

A MathML eiathony oaeaea e ionoua ioiaoee. A XML ionoua ioiaoee
eiatho aeae

<...>.

I?e iiiiue ioiaoie niaea?aeaiey MathML iiaeii iienaoue iniiaiua
iaoaiaoe/aneea

iauaeou, iaeiaei /anoi aicieeatho neooaoeee, eiaaea eniieuecothony eae
ioiaoee niaea?

aeaiey, oae e ioiaoee i?aaenoaaeaiey.

x

b

&PlusMinus

b

2

4

a

c

2

a

?anniio?ei i?eia? eniieueciaaiey ioiaoee SEMANTICS :

&int

0

t

&dd

x

x

0

t

1

x

x

3. Ioiaoee i?aaenoaaeaiey

3.1 Aaaaeaiea

3.1.1 Yeaiaiou i?aaenoaaeaiey

Yeaiaiou i?aaenoaaeaiey niioaaonoaotho eiino?oeoeeyi o?aaeeoeeiiiie
iaoaiaoe/an

eie caiene e iicaieytho iienuaaoue neioaene/aneoth no?oeoo?o
iaoaiaoe/aneiai au

?aaeaiey. Iai?eia?, no?oeoo?a This oeo/oaao ea/anoai iaoaiaoe/aneie
caiene e a

oao neo/ayo, eiaaea ia ecaanoaia, iai?eia?, ?ac?aoathuay niiniaiinoue
iiieoi?a.

3.1.2 Oeiu yeaiaioia i?aaenoaaeaiey

Yeaiaiou i?aaenoaaeaiey iiaeii ?acaeaeeoue ia aeaa eeanna : eaenaiu e
noaiu ?ac

iauaiey. Nouanoaoao oaeaea iaai? ionouo yeaiaioia, eniieuecoaiuo
aianoa n eiie?ao

iie noaiie ?aciauaiey.

Ana eaenaiu (a neioaene/aneii niunea),aeeth/aiiua a iaoaiaoe/aneia
au?aaeaiea,

aeieaeiu auoue iiia/aiu MathML ioiaoeaie eaenai. Oeiu MathML eaenai :
eaeaioeoeea

oi?u (ia?aiaiiua, eiaia ooieoeee e o.ae.),/enea, iia?aoi?u,
caa?aaeaeathuea iaoee (ia

i?eia?, e?oaeua neiaee) e no?ieiaua eeoa?aeu. Aeey i?aaenoaaeaiey
oaenoa iaiaoaia

oe/aneiai oa?aeoa?a eniieuecothony yeaiaiou eaenai.

Noaiu ?aciauaiey – eiino?oeoi?u au?aaeaiee o?aaeeoeeiiiuo
iaoaiaoe/aneeo caie

nae.

3.1.3 XML ao?eaoou

Niaeanii i?iaeoo XML ao?eaoou aeieaeiu eiaoue aeae : attr = “…”
.Ao?eaoou,/uea

cia/aiea ii?aaeaeaii eae /eneiaia, iiaoo auoue oeaeuie /eneaie eee
/eneaie n iea

aathuae caiyoie. Nouanoaotho ao?eaoou ni cia/aieyie , naycaiiuie n
ii?aaeaeaiiui

o?eooii.

3.1.4 I?iaaeu

Ii oiie/aieth XML i?ioeanni?u oaeaeytho eiia/iua i?iaaeu, neiaieu
“iiaie no?iee”,

aeeaaeee (iiceoeee oaaoeyoeee) e nie?auatho ethaia aioo?aiiaa
iacaiieiaiiia i?ino

iainoai aei iaeeii/iiai i?iaaea (” “).A neo/aa iaiaoiaeeiinoe
eniieueciaaiea auoa

ia?a/eneaiiuo neiaieia aiciiaeii iinea eo eiaee?iaaiey e oeacaiey aeey
ieo naue

eea iauaeoa.

3.1.5 O?aaoaiua ia?aiao?u

Aieueoeinoai ec iienaiiuo yeaiaioia o?aaotho ii?aaeaeaiiiai /enea
ia?aiao?ia

(1,2 eee 3).

MathML niaea?aeeo oieaa?naeueiue yeaiaio ?ayaeaeeoaey ,eaii?e?oaiue yea

iaioaie i?aaenoaaeaiey.

3.1.6 Ionoua yeaiaiou

Aaeeinoaaiiui ionoui yeaiaioii eaenaiu yaeyaony .Ionoua
yeaiaiou

e iiaoo auoue aeeth/aiu oieueei a
ii?aaeaeaiioth noaio ?ac

iauaiey.

3.1.7

Iaeioi?ua yeaiaiou, iai?eia?, eniieuecothony aeey “oe?aoaiey”
iia?aoi?ia.

3.1.8 ?acthia

Eaenaiu :

eaeaioeoeeaoi?u

iiia?

iia?aoi?

caa?aaeaeathuay iaoea

oaeno

i?iaae

eeoa?ae no?iee

Iauay noaia ?aciauaiey :

eciaiaiea noeey

aeeth/aiea niiauaiey i neioaene/aneie ioeaea

i?e nio?aiaiee ?acia?a niaea?aeaiea noaiiaeony iaaeaeeiui

ai?eciioaeueiay a?oiie?iaea ethaiai /enea iiaeau?aaeaiee

oi?ie?iaaiea ae?iae ec aeaoo iiaeau?aaeaiee

oi?ie?iaaiea ciaea eaaae?aoiiai ei?iy (?aaeeeaea aac
eiaeaena)

oi?ie?iaaiea ?aaeeeaea n ii?aaeaeaiiui eiaeaenii

Oaaeeoeu e iao?eoeu :

oaaeeoea eee iao?eoea

no?iea a oaaeeoea eee iao?eoea

iaeii aoiaeaeaiea a oaaeeoeo eee iao?eoeo

3.2 Eaenaiu

A eaenaiu iiaeii aeeth/aoue ethaia eiee/anoai neiaieia, a oii /enea
iicaieeoaeueii

eniieueciaaoue eaenaiu aac niaea?aeaiey.

3.2.1 – eaeaioeoeeaoi?u

Eaeaioeoeeaoi?u aeeth/atho a naay ia?aiaiiua, eiaia ooieoeee e
neiaieueiua eiinoai

ou.

Namevaluesdefaultfontsizenumber (points)inheritedfontweightplain|

boldinheritedfontslantplain |

italicautomaticfontfamilystringinheritedfontcolor#rrggbbinherited

Eaeaioeoeeaoi?u neiaiea Single ii oiie/aieth auaiaeyony a eo?neaiii
o?eooa, nei

aieueiua eaeaioeoeeaoi?u auaiaeyony a iaiaeeiiiii o?eooa.

x

π

D

sin

sin

&ApplyFunction;

x

Oaeno, eioi?ue ioaeii ia?aaioaoue eae neiaie, aeieaeai auoue
i?aaenoaaeai a aeaea :

1

+

+

n

3.2.2 – iiia?

eaenaiu, a ioee/ee io ,iau/ii i?aaenoaaeaiu a iaiaeeiiiii
o?eooa.

2

0.123

1,000,000

2.1e10

3.2.3 – iia?aoi?u

Eaenaiu, yaeythueany iia?aoi?aie, ioiinyony e oeio .

+

++

.NOT.

3.2.4 – caa?aaeaeathuea iaoee

Niaeaniaaiiua ia?u caa?aaeaeathueo iaoie aeieaeiu auoue aeeth/aiu a
ea/anoaa ia?ai

ai e iineaaeiaai yeaiaioia a noaio .

?anniio?ei i?eia?u au?aaeaiee, niaea?aeaueo caa?aaeaeathuea iaoee:

(a + b)

(

a

+

b

)

[0,1)

[

0

,

1

)

3.2.1.4

Iaoaieciu eniieiaiey iia?aoi?ia e caa?aaeaeathueo iaoie eaeaioe/iu e
aieaa neiae

iu ii n?aaiaieth n ae?oaeie ia?ea?aie.

Iiiaea iaoaiaoe/aneea neiaieu oeia eioaa?aeueiiai neiaiea, ciaea
“+”,e?oaeuo

neiaie e o.ae. eiatho caaeaiiua ii oiie/aieth ao?eaoou, eioi?ua iiaoo
aeeth/aoueny

a e noaiu.

Iiiaea iia?aoi?u a eaaeaeie eiie?aoiie oi?ia iiaoo eniieueciaaoueny
ii-?aciiio.

Ciae “+”,iai?eia?, a caaeneiinoe io neooaoeee iiaeao auoue eae
i?aoeenii, oae e

eioeenii.

Anee iia?aoi? yaeyaony ia?aui iiaeau?aaeaieai a e aai aeeeia
i?aauoaao

aaeeieoeo, oi eniieuecoaony i?aoeeniay oi?ia; anee aea iia?aoi?
yaeyaony iineaae

iei iiaeau?aaeaieai a ,oi i?aaeeaie i?aaeoniao?eaaaony
eniieueciaaiea iino

oeeniie oi?iu. Eioeeniay oi?ia aeey iia?aoi?ia, aeeth/aiiuo a noaio
oeia ,

ia eniieuecoaony.

Anee aicieeaao neooaoeey auai?a iaeiie ec ianeieueeeo oi?i e ia aeaii
ieeaeeo

aeiiieieoaeueiuo oeacaiee, oi i?aai aa inoaaony ca iieueciaaoaeai.

Nouanoaotho /aou?a ao?eaooa, ?aaoee?othuea niioiioaieyie iaaeaeo
?acia?aie iia

?aoi?ia ,caa?aaeaeathueo iaoie e ae?oaeo yeaiaioia : stretchy,
symmetric, maxsize

e minsize. Iai?eia?, anee aeey neiaiea maxsize=”3″,yoi icia/aao, /oi
aai ?acia?u

iiaoo i?aauneoue noaiaea?oiua ia aieaa, /ai a o?e ?aca.

?anniio?ei i?eia?: onoaiiaeoue iaeneiaeueiue ?acia? e?oaeie neiaee.

(

ab

)

3.2.5 – oaeno

Eaenaia eniieuecoaony aeey i?aaenoaaeaiey oaenoa
iaiaoaiaoe/aneiai oa

?aeoa?a.

Yoio yeaiaio /anoi eniieuecoaony aeey aeeth/aiey a aeieoiaio
“iaaeaeeiuo neiai

eia”.

Yeaiaiou, aoiaeyuea a noaiu oeia , iiaoo auoue aeeth/aiu a
noaio oeia

.

&thickspace;

a

b

I?eia?u :

Theorem 1:

&thinspace;

&alignmentmarker;&thickspace;

/* a comment */

3.2.6 – i?iaaeu

– ionoie yeaiaio, caaeathuee ionoia i?ino?ainoai ethaiai
aeaeaaiiai

?acia?a.

3.2.7 – no?ieiaue eeoa?ae

eniieuecoaony aeey aeeth/aiey a au?aaeaiey “no?ieiauo
eeoa?aeia”. nie

?auaao i?iaaeu ii oiie/aieth.

Eae i?aaeei, oaenou, eioi?ua iaiaoiaeeii aiaae?eoue a iaoaiaoe/aneee
aeieoiaio,

/aua aeeth/athony a noaiu oeia ,,,a ia a noaiu oeia
.

No?ieiaua eeoa?aeu ioia?aaeathony caeeth/aiiuie a aeaieiua eaau/ee.

” iiaeii
i?aaenoaaeoue eae :

there exists

δ

>

0

such that

f

&af;

(

x

)

<

1

3.3 Iauay noaia ?aciauaiey

Iiieii eaenai nouanoaoao ianeieueei naiaenoa yeaiaioia i?aaenoaaeaiey
MathML.

Iaeii ec oaeeo naiaenoa naycaii n ?acee/iuie noaiaie nicaeaiey
noeaia?eaa, ae?o

aia – n oaaeeoeaie e iao?eoeaie. Nouanoaotho yeaiaiou, n /ueae
iiiiuueth iienuaathony

iniiaiua noaiu caiene ae?iaae, ?aaeeeaeia e o.ae., i?ienoiaeeo iiene e
ia?aaioea

ioeaie e i?.

3.3.1 – eciaiaiey noeey

eniieuecoaony aeey aianaiey eciaiaiee a niaea?aeaiea.

I?eia? eciaiaiey ?acia?ia e?oaeie neiaee, caienaiiue n eniieueciaaieai
e

,iiaeii ia?aienaoue n neaaeothuei ia?acii:

(

ab

)

3.3.2 – aeeth/aiea niiauaiey ia ioeaeao

Niiauaiea i neioaene/aneie ioeaea iiaeao auoue i?iecaaaeaii iooai
eciaiaiey

oiiiaiai oeaaoa, aunaa/eaaiey ecia?aaeaiey eee iiae/a?eeaaiey ioeaee
e?aniui

oeaaoii.

Caaea/a yoiai yeaiaioa ninoieo a iaania/aiee iaoaiecia niiauaiey i
neioaene

/aneeo ioeaeao i?e niaianoiie ?aaioa MathML n ae?oaeie i?eeeaaeiuie
i?ia?ai

iaie.

3.3.3.

iiaeao eniieueciaaoueny aeey au?aaieaaiey /anoae
au?aaeaiey e eciaia

iey iiceoeee neiaieia.

3.3.4 – ai?eciioaeueiay a?oiie?iaea iiaeau?aaeaiee

Ianeieueei iia?aoi?ia iiaoo auoue aeeth/aiu a noaio oeia
oieueei a oii

neo/aa, eiaaea iie i?eiaaeeaaeao e iaeiiio oeio.

A?oiie?iaea i?aneaaeoao neaaeothuea oeaee: oeo/oaiea aecoaeueiiai
i?aaenoaaeaiey

e oi?iuaiea ia?aaioee eioi?iaoeee ?acee/iuie n?aaenoaaie,
i?aaeiacia/aiiuie aeey

yoie oeaee.

I?eia? iiaeao auoue
caienai

oae:

2

&InvisibleTimes;

x

+

y

z

3.3.5 – oi?ie?iaaiea ae?iae ec aeaoo iiaeau?aaeaiee

numerator(ciaiaiaoaeue) denominator(/eneeoaeue)

3.3.6 e – oi?ie?iaaiea ?aaeeeaeia

Noaia eniieuecoaony aeey auaiaea eaaae?aoiuo ei?iae, a noaia

– aeey auaiaea ?aaeeeaeia n eiaeaenaie.

base

base index

3.4

Aeey eo/oae oeenaoeee aano?aeoiie no?oeoo?u caiene MathML
iaania/eaaao niaoeea

eece?iaaiioth noaio nicaeaiey noeaia?ey.

Ioiaoee i?aaenoaaeaiey eniieuecothony iienaiey no?oeoo?u au?aaeaiee.

iiaeao auoue
i?aaenoaaeaii a

neaaeothuai aeaea:

(

x

+

y

)

2

3.4.1

base subscript

3.4.2

base superscript

3.4.3

base subscript superscript

Eioaa?ae i?e iiiiue iiaeii caienaoue neaaeothuei ia?acii :

0

1

&ee;

x

&it;

&dd;

x

3.4.4

base underscript

3.4.5

base overscript

3.4.6

base underscript overscript

PAGE

PAGE 14

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