G.H. Hardy

absolutely convergent algebraical function angle assumes ax+b ax² ax²+2bx axis bounded function circle complex numbers condition consider continuous function convergent corresponding cos² curve decimal deduce defined definition denote derivative discontinuous displacement divergent equal equation example expressed finite number formula geometrical graph greater Heine-Borel theorem Hence inequality infinitely infinity integral values interval inverse function less limit Math maxima and minima mean value theorem n≥no obtain oscillates finitely polynomial positive integer positive number positive or negative positive values proof Prove rational function rational numbers reader real numbers recurring decimal result satisfied Show Similarly sin² straight line sufficiently large values suppose tangent tends to zero Trip values of x vanishes variable write x+yi x₁