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X } g r ONE1ml X } g r K X R e B O V R ^ C v/1ml iJAN R h j ̃y W ł B i 2 `3 c Ɠ ȓ ɔ ܂ i y j j B DCM I C ̓V V A C Ђ̃K X R e B O w z Z ^ ʔ̃T C g ł BDCM I C ł̓J p i ͂ ߂Ƃ A 34 _ ̏ i 舵 Ă ܂ B z Z ^ ʔ DCM I C ł̂ y ݂ BN=1 g n(x) converges absolutely by Theorem 266 (Ratio Test), and so lim n!1 g n(x) = 0 by Theorem 223 So fg ngconverges pointwise to the zero function By the comments after De nition 603, if fg ngwere to converge uniformly on 0;1, then it would need to converge to the zero function However, note that g n(1 n) = (1 n) n ThereforeAnd z2 = 2b 2y2, so x2 z = 2a 2y2 2b y2 = 2a2b 2y = 2(ab y2)Since a b 2y 22Z, x z is even and so xRzTherefore, R is transitive The distinct equivalence classes of R are 0 = fx 2Z x is eveng 1 = fx 2Z x is oddg We see that these are the only distinct equivalence classes of R because we have proven

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