Poove j-2 A diveoges using

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.1: Sets
Problem 38E: 38. Prove or disprove that .
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Please solve hw-3. By using given theorem. Thanks 

Theorem: if Eaj convenges then
Proof
O Ž aj conuorgJes
O Given
O{S, = Eg IneW}is Cauchy
©S ancdy
® Conuerges
%3D
Odefn
Nzw'uA gis NE O<3A @
of
Cuachy
☺
| Smti-Sml<E ☺ Taking n=mel
4,
(S)
| amril< E ☺
+ mt amtl
+ Am ) =
mt)
3.
☺ by steps 3-5
O VE>O Choose N;= Nil so
O lim a
つ
=0 ® Defnof
limit
QED
Transcribed Image Text:Theorem: if Eaj convenges then Proof O Ž aj conuorgJes O Given O{S, = Eg IneW}is Cauchy ©S ancdy ® Conuerges %3D Odefn Nzw'uA gis NE O<3A @ of Cuachy ☺ | Smti-Sml<E ☺ Taking n=mel 4, (S) | amril< E ☺ + mt amtl + Am ) = mt) 3. ☺ by steps 3-5 O VE>O Choose N;= Nil so O lim a つ =0 ® Defnof limit QED
Hw3 Poove
a diveoges using
proof by
contradiction
a
and attached the orem
Transcribed Image Text:Hw3 Poove a diveoges using proof by contradiction a and attached the orem
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