Answer to Question #32173 in Real Analysis for shamika

Question

1) in the system of real numbers the axiom of existence of additive inverse states that, for all x element of R there exists y element of R such that x+y=y+x=0. prove that the additive inverse(y) corresponding to each real number x is unique. what can you say about the statement, there exists y element of R such that for all x element of R x+y=y+x=0?

2)if a and b are irrational numbers is, a to the power of b necessarily an irrational number? prove your claim

3)suppose A,B,C,D are four distinct points with position vectors a,b,c,d respectively, show that A,B,C,D lie on a plane if and only if there exists w,x,y,z element of R such that w+x+y+z=0 and aw+bx+cy+dz=0

Answer 1

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