Let y epsilon R Prove that 0 lessthanorequalto y y Solution

Let y epsilon R. Prove that 0 lessthanorequalto y - [y]

Solution

(a) We know that x1< x x thus after multiplying by -1 in this eqn we get,

-x< -x 1-x, adding x in this relation we get, 0<x-x1,PROVED..

(b)

in this part you didnot tell about notion D . i dont know what is D here..

(c) same as (b ) part prob.

but i am telling you the method of proving . as we know D contain in D(CLOSURE), so we have to show only that if x does not belong to D then x belong to D (closure ) also. take any arbitray point x then find a nbd of x whose intersection is non empty with D

that the process to prove