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Why i(3^0) = i(3^8) = 0.please with explanation. I think 3^0 is always 0 . (3 is the notation , not number)

Why i(3^0) = i(3^8) = 0.please with explanation. I think 3^0 is always 0 . (3 is the notation , not number)

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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Why i(3^0) = i(3^8) = 0.please with explanation. I think 3^0 is always 0 . (3 is the notation , not number)
a*b atb ab k a米の米-、米a ka - 1 - a There is an somorphism of Ug mith Zg in which 3=e' Find the ekment in Zs hat coresponds to 3" for cach M=0,1, - Let i Ug-)Zg be the isormorphism where il7)=5 By te lomormuphiom paperty d ismphins il7)= i(3 3) = i(7) -, (3) = 5+,5 - 2 %3D i(7') = il7") +, i(7) = 2+5 = 7 i(7") = i(7') +s i(7) = 7+g 5=4 i(3) = il7")*s i(3)= 4 +5=1° il7)= il7)+, il7)= 1l+, 5 = 6 i(3*)= i(3")*n i(3)= G t3 5- 3 i(3") = i(3?) = ¿(3")te il3)= 3+, 5 = 0 0 Def: Let <G, ,,) sd <Gs, B) be geaps and f.G,>G- We say fis (1) f ó a bijective mp (a) for all a,beG,, flax, b)= f(=) x, f(b), [0,6) Lo, c) Ex: Find a bijective furction fram Ry to R. for any b,ce R". Hence R.R su for ceR my Let f: Ry-7R be defined as f(t)= g (t) Injecine : Let toste ER and suppre fit.) -flt,) Sajective: Sappose D c, R..
Transcribed Image Text:a*b atb ab k a米の米-、米a ka - 1 - a There is an somorphism of Ug mith Zg in which 3=e' Find the ekment in Zs hat coresponds to 3" for cach M=0,1, - Let i Ug-)Zg be the isormorphism where il7)=5 By te lomormuphiom paperty d ismphins il7)= i(3 3) = i(7) -, (3) = 5+,5 - 2 %3D i(7') = il7") +, i(7) = 2+5 = 7 i(7") = i(7') +s i(7) = 7+g 5=4 i(3) = il7")*s i(3)= 4 +5=1° il7)= il7)+, il7)= 1l+, 5 = 6 i(3*)= i(3")*n i(3)= G t3 5- 3 i(3") = i(3?) = ¿(3")te il3)= 3+, 5 = 0 0 Def: Let <G, ,,) sd <Gs, B) be geaps and f.G,>G- We say fis (1) f ó a bijective mp (a) for all a,beG,, flax, b)= f(=) x, f(b), [0,6) Lo, c) Ex: Find a bijective furction fram Ry to R. for any b,ce R". Hence R.R su for ceR my Let f: Ry-7R be defined as f(t)= g (t) Injecine : Let toste ER and suppre fit.) -flt,) Sajective: Sappose D c, R..
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