Recent content by cpl1992

  1. C

    I solving a proof dealing with the set of irrational numbers.

    Homework Statement Let x,y,t be in the set of all real numbers (R) such that x<y and t>0. Prove that there exists a K in the set of irrational numbers (R\Q) such that x<(K/t)<y Homework Equations if x,y are in R and x<y then there exists an r in Q such that x<=r<y The Attempt at a...
  2. C

    I solving a proof relating sup(AB) and Binf(A)

    I still seem to be confused as to how B would relate to the elements in the set. If B is sup(A) then this is saying it is the lowest upper bound of A. If this is the lowest upper bound then B could be either less than or greater than the set of BA itself correct?
  3. C

    I solving a proof relating sup(AB) and Binf(A)

    Supremum is the lowest upper bound of the set and infimum is the highest lower bound of the set
  4. C

    I solving a proof relating sup(AB) and Binf(A)

    Homework Statement Let A be a bounded nonempty subset of the set of all real numbers (R). B exists in R and B<0. Let BA= {Ba: a exists in A} Prove sup(BA)=Binf(A) Homework Equations We are able to use the ordered field axioms, Archemedian Property ect..The Attempt at a Solution I know that...