M3220-1 Sixth Homework Assignment

MATH 3220 § 1 SIXTH HOMEWORK ASSIGNMENT Due Thursday,

A. Treibergs March 10, 2005

MATH 3220 § 1	SIXTH HOMEWORK ASSIGNMENT	Due Thursday,
A. Treibergs		March 10, 2005

Please hand in the following exercises from the text "An Introduction to Analysis, Third Edition" by William Wade, Prentice Hall, 2004.

262[ 1c, 3, 8 ]

Please hand in the additional exercise.

Let E be a subset of R. How many different sets can be obtained from E by taking closure or complementation? Prove your answer. If we denote closure by E^- and complement by E^c, then the question is: at most how many different sets can occur in the sequence

..., E^-c-, E^-c, E^-, E, E^c, E^c-, E^c-c,... [This problem was first assigned in HW 5. Its due date is extended.]

Please hand in the following exercises from the text "An Introduction to Analysis, Third Edition" by William Wade, Prentice Hall, 2004.
262[ 1c, 3, 8 ]
Please hand in the additional exercise.
Let E be a subset of R. How many different sets can be obtained from E by taking closure or complementation? Prove your answer. If we denote closure by E^- and complement by E^c, then the question is: at most how many different sets can occur in the sequence ..., E^-c-, E^-c, E^-, E, E^c, E^c-, E^c-c,... [This problem was first assigned in HW 5. Its due date is extended.]