# Simplex: outgoing variable cannot re-enter the basis next iteration

How can I prove that in the simplex method, a variable that has just left the basis cannot re-enter the basis on the very next iteration? The pivoting rule is Dantzig's.

• what is the pivot rule? Jun 14 '12 at 16:00
• with danzig rule thanks! Jun 15 '12 at 14:38

• that the variable's $z_j - c_j$ becomes nonnegative in the next iteration?