MATH15910 THEOREMS Rational
numbers
Q
Def function A Bis
T.FI
ii
asubsetfcaxbs.t.vae .a.name
at
ofa
Property
fiiiiiitiii s
of inverse
existence multiplicative
aaoameaa.im
Def
seaispositivei abso.at
Det haealaso
fifI iIIsea
c.ms
2surjjfi.it
aeast.flatb iiii i
3bid eltive
and
s urjective DefAnordered
field
hastheleastupperboundpropertyi forever0
sc there
thatisboundedfromabove exists
aleastupperbound.supremumsupcss at
1 i iiiiinat Iics sthii.iii Remark.im aaiinbelow
Iii t Ijection
FAB
Axiom
Bif it
afiathathastheleastupperboundproper Detth
it ijethnI15 Archimedean
property
Thm
m
In.int n isnotboundedtomabore
corn
it i ets.t.nana
i'iii.itiiii.ii
i iiiii iiiiiiii.it
i ii it
Propertiesof2x2
2
associativityacbascabs
commutativityiab
b oamultiplicativeunitia1ezs.t.al
a
fi ti ihaaltlbl
comm
fiiiiiii.ci iabta Thm kt.Inen'v
o.aeas.t.ir.ae
iiiiiiiii.it
iii.IE iiiii iii.iei i i
Defaeiristhelimitofcaisie if
vesoanoezast.lanalcev.mn
caisconvergesifithasalim.it
Propifcanconverges.thencanisaca.chsequence
thmiifcanisaca.ch thenitconvergescinirs
sequence
iiiiiii.iti
Lemmamultiplicative
Archimedean
property
iflaki.thenv.no
ns.t.lanklaice
if main
numbers
Q
Def function A Bis
T.FI
ii
asubsetfcaxbs.t.vae .a.name
at
ofa
Property
fiiiiiitiii s
of inverse
existence multiplicative
aaoameaa.im
Def
seaispositivei abso.at
Det haealaso
fifI iIIsea
c.ms
2surjjfi.it
aeast.flatb iiii i
3bid eltive
and
s urjective DefAnordered
field
hastheleastupperboundpropertyi forever0
sc there
thatisboundedfromabove exists
aleastupperbound.supremumsupcss at
1 i iiiiinat Iics sthii.iii Remark.im aaiinbelow
Iii t Ijection
FAB
Axiom
Bif it
afiathathastheleastupperboundproper Detth
it ijethnI15 Archimedean
property
Thm
m
In.int n isnotboundedtomabore
corn
it i ets.t.nana
i'iii.itiiii.ii
i iiiii iiiiiiii.it
i ii it
Propertiesof2x2
2
associativityacbascabs
commutativityiab
b oamultiplicativeunitia1ezs.t.al
a
fi ti ihaaltlbl
comm
fiiiiiii.ci iabta Thm kt.Inen'v
o.aeas.t.ir.ae
iiiiiiiii.it
iii.IE iiiii iii.iei i i
Defaeiristhelimitofcaisie if
vesoanoezast.lanalcev.mn
caisconvergesifithasalim.it
Propifcanconverges.thencanisaca.chsequence
thmiifcanisaca.ch thenitconvergescinirs
sequence
iiiiiii.iti
Lemmamultiplicative
Archimedean
property
iflaki.thenv.no
ns.t.lanklaice
if main
