Ch
2
s
2
2 1
.
.
The
-
1
.
-
Algebraic
-
1
Real Numbers
and order
1R
Algebraic propertions of
All 了
a
b
+
b
=
a
+
Ha
,
1R
propertions of
,
bEIR
adding
(A
2
]
latb }
C
+
(A3)
J bEIR
LA 4 )
HGER
+
t
G
=
b
+
called …
,
"
)
0
t a
,
,
"
b
,
Ss t
CE ) R
,
O + a
.
.
-
aER
such
a
[
+
a
=
,
F
,
c
a
-
]
VGE 1 R
,
=
0
multiBy
(M
1
Ha
)
bE 1 R
,
( M 2)
Va
( M3 ) A
CEO E
(M 4)
V afo
(D )
V
a
,
a
,
.
,
b
,
a
2 1
.
.
E 1R
E 1R
Ad
,
a
,
I unique
2
la )
Let
Et 1 R
( b)
Let
Ut
lc )
Ha
Proof
:
a
ε
)
IR
be
1
,
,
R
a
.
0
Consider
b)
.
.
and
Theorem
a
.
“
Called
1 R,
c
b
=
(
b ct 1 R
,
b
if
=
1
c
a
=
"
s t
,
.
FO E 1 R
( b
+
c
(
b +
c
)
a
)
V
.
(
a
,
if
V
Hb
EIR
0
t 0
)
aE 1 R
b)
.
( b
=
.
a
G
.
=
la
+
(
-
a
"
a
,
+
)
1
,
a
"
a 1 R , zta =
,
ub
=
0
2
c
.
Called
,
=
b
(
.
c
c
.
-
at
:
)
a
)
identities )
of
given
.
=
2
by
(A
3)
b
a
,
, then
then
u
=
1
220
1
By
A 4)
2
,
2
=
by
(A
+ 0
]
2
2
=
( Z
=
1
+
+
a
a
]
a
lagypothesis
+
=
by
b)
)
Exercie
Consider
( M 33
a
=
( D)
=
( A 33
=
=
a
.
0
=
0
a
+
G 1
G
G
.
+
(
1 +
0
.
G
0
.
0
)
以
G
by part
la )
( A Ψ]
=
0
+
+
(
-
(
a
-
)
)
a
)