caNverges. roctice 4. show thast a CHint, stmcler idea utth irts diaraslng sequence cuuerges.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 48E: Let R be the set of all infinite sequences of real numbers, with the operations...
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Thm l0.2 All kounded mawstene sequences Comverge.
- sups
pf. Let (5) be a bounded nerensing. sequenco.
Shce (Su) kunded, the set of olues S ue is kanded.
Ey the complotmoes atom. say U= sup S.
Claine : Sn = u.
Gluen E70 N GN st
u-E < SN
: k- sup S
n7N = u-ɛ < Sus Sn
and
U-eく Sn Suくu+を
Froctce 4. show thast a
CHint, Sstmilar idea utth irts )
diarosing squence canuerges.
Transcribed Image Text:Thm l0.2 All kounded mawstene sequences Comverge. - sups pf. Let (5) be a bounded nerensing. sequenco. Shce (Su) kunded, the set of olues S ue is kanded. Ey the complotmoes atom. say U= sup S. Claine : Sn = u. Gluen E70 N GN st u-E < SN : k- sup S n7N = u-ɛ < Sus Sn and U-eく Sn Suくu+を Froctce 4. show thast a CHint, Sstmilar idea utth irts ) diarosing squence canuerges.
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