Question

1. Write the set {x:xe R. -4<x<=6) as an interval​

Answer 1

Answer:

Transcribed Image Text from this Question

(x E R | 0 < x < 1} and let 10. Let J be the unit open interval. That is, J S = {(x,y) E R × R | 0 < x < 1 and 0 < y < 1 }. We call S the unit open square. We will now define a function f from S to J. Let (a,b) e S and write the decimal expansions of a and b in normalized form as b - O.bib2b3b4...bn ..- We then define f(a. b) -0.ajbia2b2a3b3a4b4..-anbn (a) Deterirae the values of f0.3,0.625). /(. (b) If possible, find (xE S such (c) If possible, find (d) ssible, find(x, y) e S such that f(x, у (e) Explain why the function f:S-»J is an injection but is not a surjec- (f) Use the Cantor-Schröder-Bernstein Theorem to prove that the cardi- 6'6 0.2345. (x,y) 2 tion. nality of the unit open square S is equal to c