We covered countability and induction in the last week. For the countability part, we got a very tricky question at the lecture. It asks if X={natural numbers} has the same size as Y={even natural numbers}. Intuitively thinking, X contains 0,1,2,3,4,5...... and Y contains only 0,2,4,6.....so X's size is larger than Y's. BUT, THAT IS WRONG!!!! In fact they have the same size! It was quite confused to me but it make sense after Larry's explanation. We can think in this way, say X={number of coin in the world}, Y={number of tail of coin in the world}, then it is easy to see that these two sets have the same size, since each coin has one and only on tail, so the number of coin must be equal to the number of tail.
The second part of lecture involves the introduction of induction. Induction is a very important tool in mathematic proof. When we get several special case for some NATURAL number, we may possible to prove some properties for all natural number. This is called the induction, The following is an general example in class.
The last part of the lecture was about the review for the final exam.
That's all for week 12. Good luck everyone on your final exam!!!
Hello, this is your TA, good work on your SLOGs. I hope you enjoyed the course. Good luck on the final!
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