66 pitcher: interrelations of 



(I 14) A° . 2)?^' + [0] . 3 . aif^"-. § 41.15. § 48a6. 

 (I 15) A^'' . g)?^- + [0] . 3 . ai?'^'- . § 41.15. § 4865. 



(IIi2 1) singular or dual. 



(IIi2 2) A . 9j;"^^='^'-"^"- . 3 . 2)J"^'^ §42.2. § 48g2. 



(IIioS) A . 5m^^="^-"^=" . 3 . 9DJ"^'=-. §42.3. § 48g2. 



(IIi2 4) A° . m^"''''' . D . m''". § 42.4. § 48/6. 



(IIi2 5) A"^'''.5D?^-^''^'=.D.9[»?^-. §42.5. § 48g3. 



(IIi2 6) A"^'° .3)1^^ .z>. dJl-\ § 42.6. § 48/6. 



(IIi2 7) A° . g??'^"^^ 3 . a»J^\ § 42.7. § 48/6. 



(IIi2 80 A''"' . W""' . z> . 9??^'-. § 42.8.. § 48^9 ({ = 1, 2, 12). 



(IIi23 1) singular, dual or triple. 



(IIi23 2) A.9[l^^^^'^^D.9[l^'^''•-»^^^•. §43.1. §48g4. 



(11123 3) A.5Dr^^'''^=^'=-.3.9[ir"^9JJ^=-. §43.2. §48^4. 



(II 1) finite. 



(II 2) A^ . 3«^"^- . 3 . yjl"": § 44.4. § 48^10. 



(II 3) A^ . m^"'"' . 3 . Tl''": § 44.5. § 48^10. 



49&. Characterizations of developments A. — 



(1) A''' : ~ : A a g}J . 3 . Wl\ 



(2) A^' : ~ : A 9 2JJ . 3 . S;)?^^. 



(3) A^' : ~ : A 9 9}J . 3 . 93J^\ 



(4) A'^' : cv. : A 9 5W^= . 3 . W": 



These follow from § 17; § 20a2; § 20al and from the jaropositions : 



(1') A-'''.3. 3 9}r^; 



(2') A"^' . 3 . 3 9[)r^- 



(3') A'^' .3.3 9.1?^'"^'=. 



49c. Characterizations of classes of functions * — • 



(1) 2« ^ [0] : ~ : a« 9 A . 3 . 9JJ'^'. 



(2) 9[»J 9 M • 3 . m"'"''"""'-' : ~ : g« 9 a . 3 . Wl"'. 



50. In the Introduction to a Form of General Analysis it is shown 

 that the propertj- iv,,^ is implied by the properties D, A, Ki, K-, and 

 that the properties ivi, K-> are implied by i^i,*-! However examples 



* Cf. I. G. A., pp. 130. 



t § 23al7, II12; I. G. A., § 82II; § 72all,,. 



