= Ek=0 for each n = 0,1,2,3 .…. Let X = {Sn]n = 0,1,2,3 ……} and Let Sn = EIn = 1,2,3 -.}U {0}. Let f:X → Y be a function defined by f (sSn) =- if n = 1,2,3 .., and f(so) = 0. Since fis 1-1 and onto, f -1: X → Y is a function. Is f -1 continuous at 0? Use the ɛ – 8 definition of continuity (or limit of a function) to prove your claim. No proof by contradiction, please.
= Ek=0 for each n = 0,1,2,3 .…. Let X = {Sn]n = 0,1,2,3 ……} and Let Sn = EIn = 1,2,3 -.}U {0}. Let f:X → Y be a function defined by f (sSn) =- if n = 1,2,3 .., and f(so) = 0. Since fis 1-1 and onto, f -1: X → Y is a function. Is f -1 continuous at 0? Use the ɛ – 8 definition of continuity (or limit of a function) to prove your claim. No proof by contradiction, please.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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