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...
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?
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...