英语四则运算表达方式

1.Logic

∃thereexist

∀forall

p⇒qpimpliesq/ifp,thenq

p⇔qpifandonlyifq/pisequivalenttoq/pandqareequivalent

2.Sets

x∈AxbelongstoA/xisanelement(oramember)ofA

x∉AxdoesnotbelongtoA/xisnotanelement(oramember)ofA

A⊂BAiscontainedinB/AisasubsetofB

A⊃BAcontainsB/BisasubsetofA

A∩BAcapB/AmeetB/AintersectionB

A∪BAcupB/AjoinB/AunionB

A\BAminusB/thediferencebetweenAandB

A×BAcrossB/thecartesianproductofAandB

3.Realnumbers

x+1xplusone

x-1xminusone

x±1xplusorminusone

xyxy/xmultipliedbyy

(x-y)(x+y)xminusy,xplusy

xyxovery

=theequalssign

x=5xequals5/xisequalto5

x≠5x(is)notequalto5

x≡yxisequivalentto(oridenticalwith)y

x≡yxisnotequivalentto(oridenticalwith)y

x>yxisgreaterthany

x≥yxisgreaterthanorequaltoy

x<yxislessthany

x≤yxislessthanorequaltoy

0<x<1zeroislessthanxislessthan1

0≤x≤1zeroislessthanorequaltoxislessthanorequalto1

|x|modx/modulusx

x2xsquared/x(raised)tothepower2

x3xcubed

x4xtothefourth/xtothepowerfour

xnxtothenth/xtothepowern

x−nxtothe(power)minusn

x(square)rootx/thesquarerootofx

x3cuberoot(of)x

x4fourthroot(of)x

xnnthroot(of)x

(x+y)2xplusyallsquared

(xy)2xoveryallsquared

n!nfactorial

x^xhat

xxbar

x˜xtilde

xixi/xsubscripti/xsuffixi/xsubi

∑i=1naithesumfromiequalsonetonai/thesumasirunsfrom1tonoftheai

4.Linearalgebra

‖x‖thenorm(ormodulus)ofx

OA→OA/vectorOA

OAOA/thelengthofthesegmentOA

ATAtranspose/thetransposeofA

A−1Ainverse/theinverseofA

5.Functions

f(x)fx/fofx/thefunctionfofx

f:S→TafunctionffromStoT

x→yxmapstoy/xissent(ormapped)toy

f'(x)fprimex/fdashx/the(first)derivativeoffwithrespecttox

f''(x)fdouble-primex/fdouble-dashx/thesecondderivativeoffwithrespecttox

f'''(x)triple-primex/ftriple-dashx/thethirdderivativeoffwithrespecttox

f(4)(x)ffourx/thefourthderivativeoffwithrespecttox

∂f∂x1thepartial(derivative)offwithrespecttox1

∂2f∂x12thesecondpartial(derivative)offwithrespecttox1

∫0∞theintegralfromzerotoinfinity

lim⁡x→0thelimitasxapproacheszero

lim⁡x→0+thelimitasxapproacheszerofromabove

lim⁡x→0−thelimitasxapproacheszerofrombelow

logeylogytothebasee/logtothebaseeofy/naturallog(of)y

ln⁡ylogytothebasee/logtothebaseeofy/naturallog(of)y