Bounds on rational approximations of numbers with this property were refined by Thue, Siegel, and Roth. Bounds on approximations (10[1])of numbers with this property use that this property is [emphasize] not possessed by the infinite sum of one over “10 to the (10[1])k factorial.” If (10[2])a-sub-i are (-5[1])distinct numbers with this (10[1])property, then “e to the (-5[1])a-sub-i” are (-5[1])independent over the rationals. A field extension has this property if it (10[1])has finite (10[1])degree. A (10[1])number was shown [emphasize] not to have this property when a simplified version of (-5[1])the Lindemann–Weierstrass theorem (10[1])was used (10[1])by (10[1])Charles Hermite. All rationals and some irrationals like (10[1])the golden (10[1])ratio belong to the countable set of numbers (10[1])with (-5[1])this property. For 10 points, name this property of numbers that are the roots (10[1]-5[1])of (-5[1])polynomials with rational (10[1])coefficients, (10[1])which is contrasted (10[1])with being (10[5])transcendental. ■END■