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(=) Assume I + a = I + b. .. a El + a :: a El + b : a = i + b for some i EI .. i = a – b .. a – bE I (E) Assume a - bEI Assume x E I + a .: x = i + a for some i EI . x = i + a + (-b+ b) : x = (i + a – b) + b .. x E I + b .. I + a CI + b Assume x E I + b .: x = i + b for some i E I :: x = i +b + (-a + b) .x = (i + b – a) + a .. x EI + a .. I +b CI+a .: I + a = 1 + b

(=) Assume I + a = I + b. .. a El + a :: a El + b : a = i + b for some i EI .. i = a – b .. a – bE I (E) Assume a - bEI Assume x E I + a .: x = i + a for some i EI . x = i + a + (-b+ b) : x = (i + a – b) + b .. x E I + b .. I + a CI + b Assume x E I + b .: x = i + b for some i E I :: x = i +b + (-a + b) .x = (i + b – a) + a .. x EI + a .. I +b CI+a .: I + a = 1 + b

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Justify each claim of the proof
(=) Assume I + a = 1 + b. .. a El + a :: a El + b . a = i +b for some i E l .. i = a – b .. a – bE I (E) Assume a – b € I Assume x E I + a .: x = i + a for some i EI .. x = i + a + (-b+b) : x = (i + a – b) + b .. x E I + b .. I + a CI + b Assume x E I + b .: x = i + b for some i E I : x = i + b + (-a + b) .x = (i + b – a) + a .. x EI + a .. I +b CI+a .: I + a = 1 + b
Transcribed Image Text:(=) Assume I + a = 1 + b. .. a El + a :: a El + b . a = i +b for some i E l .. i = a – b .. a – bE I (E) Assume a – b € I Assume x E I + a .: x = i + a for some i EI .. x = i + a + (-b+b) : x = (i + a – b) + b .. x E I + b .. I + a CI + b Assume x E I + b .: x = i + b for some i E I : x = i + b + (-a + b) .x = (i + b – a) + a .. x EI + a .. I +b CI+a .: I + a = 1 + b
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