▁early ▁Indian ▁mathemat icians ▁since ▁Man ava ▁, ▁who ▁were ▁aware ▁that ▁the ▁square ▁roots ▁of ▁certain ▁numbers ▁such ▁as ▁ 2 ▁and ▁ 6 1 ▁could ▁not ▁be ▁exactly ▁determined . ▁Ar ound ▁ 5 0 0   BC , ▁the ▁Greek ▁mathemat icians ▁led ▁by ▁P yth ag or as ▁realized ▁the ▁need ▁for ▁ir r ational ▁numbers , ▁in ▁particular ▁the ▁ir r ational ity ▁of ▁the ▁square ▁root ▁of ▁ 2 . ▁ ▁The ▁Middle ▁A ges ▁brought ▁the ▁accept ance ▁of ▁zero , ▁negative , ▁integral , ▁and ▁fraction al ▁numbers , ▁first ▁by ▁Indian ▁and ▁Chinese ▁mathemat icians , ▁and ▁then ▁by ▁Arab ic ▁mathemat icians , ▁who ▁were ▁also ▁the ▁first ▁to ▁treat ▁ir r ational ▁numbers ▁as ▁algebraic ▁objects , ▁which ▁was ▁made ▁possible ▁by ▁the ▁development ▁of ▁algebra . ▁Arab ic ▁mathemat icians ▁merged ▁the ▁concepts ▁of ▁" number " ▁and ▁" m agn itude " ▁into ▁a ▁more ▁general ▁idea ▁of ▁real ▁numbers . ▁The ▁Egypt ian ▁math ematic ian ▁Ab ū ▁K ā mil ▁Sh uj ā ▁ibn ▁As lam ▁ ▁was ▁the ▁first ▁to ▁accept ▁ir r ational ▁numbers ▁as ▁solutions ▁to ▁quadratic ▁equations ▁or ▁as ▁coefficients ▁in ▁an ▁equation , ▁often ▁in ▁the ▁form ▁of ▁square ▁roots , ▁cube ▁roots ▁and ▁fourth ▁roots . ▁ ▁In ▁the ▁ 1 6 th ▁century , ▁Simon ▁Ste vin ▁created ▁the ▁basis ▁for ▁modern ▁decimal ▁notation , ▁and ▁ins isted ▁that ▁there ▁is ▁no ▁difference ▁between ▁rational ▁and ▁ir r ational ▁numbers ▁in