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its been quite sometime since i last login here to write something.... even for now i dont have apparent time and more importantly enough persistent thoughts to write anything worth reading so heres this rather a small problem i ve been stuck on quite sometime... its mathematics down below ... anyone allergic please leave now its a question of infinite series ... if : x = 1-1+1-1+1-1+1-.......... infinity then whats the possible value of x now heres what i first thought .... if we separate all positive and negative ones then problem would rearrange in following manner x = ( 1+1+1+1 .... infinity ) - ( 1+1+1+1+ ... infinity ) x = infinity - infinity = either ( infinity ) or ( not defined ) but theres another approach if x = 1-1+1-1+1- .... = 1- (1+1-1+1-1+1-1+....) = 1 - x => 2x = 1 => x = 0.5 !!!!! it seems to be and in fact is more satisfying mathematical answer. for one fact it save us from dealing with infinity .. but what concerns me is where did i go wrong in first place .... it was simple rearranging of the equation ... theres no mathematical anomaly there ..so why this paradox... if u have any answers...!!