For any odd positive integer n, the equation .v4 = (namely x = -1)34 e introduce the predicate Pta, n)= "the equation f = -1 has a as a root: where the domain of discourse is the. set of all real...

For any odd positive integer n, the equation .v4 = (namely x = -1)34 e introduce the predicate Pta, n)= "the equation f = -1 has a as a root: where the domain of discourse is the. set of all real numbers for a, and the set of all odd positive intems for n. We can easily represent the fact that x" = -1 has a real root (existence only) symbolically as: Vn 3a Na, n). If we wanted to represent the complete existence and uniqueness statement, it would run something like this: n Pati [P(a,n) A Vb ((b * a) -4 - P(b, ti))1. Mathematicians have invented the shorthand notation 3! for existence and uniqueness With this new symbol, the theorem can be succinctly represented symbolically as 'in 2!a Pta.n).
haS a unique real root.