Section 10.5 up to Theorem 10.18, Due on Wednesday March 19th

The Schröder-Bernstein Theorem

What was difficult for me?  Nearly everything.  Well, at first.

Then I took a step back and really thought about what this theorem was saying.  This allowed me to clear my thoughts and think about what this was really asking.  It's really simple.  If the cardinality of set A is less than or equal to the cardinality of set B, and the cardinality of set B is less than or equal to the cardinality of set A, then the cardinality of set A must be equal to the cardinality of set B.  That's the only thing that makes sense.  You can't have two sets that are BOTH less than each other.  This theorem actually makes a lot of sense when you sit back and think.

The most difficult part of this reading was the reading leading up to the various theorems (lemma 10.16, theorem 10.17).  It was difficult to read through these.  But, it all started making sense once I took a step back.  

What was the most interesting for me?  I like the simplicity of this theorem.

There is a part of the reading, Theorem A, that says "For every two sets A and B, exactly one of the following occurs: (1) |A|=|B|, (2) |A| < |B|, (3) |A|>|B|."  This contains a lot of truth.  When comparing two things, either one is greater and one is less, or they are equal.  There is no disputing this.  This is always true, even though we might not have the information to prove that this is true, meaning, we aren't sure about the characteristics of the sets.  When we know about the sets, we can tell some important things about them - what is greater, lesser, or if they're equal.  It will now be interesting to prove this.