In your own words, what does it mean if two sets have the same cardinality?

An uncountable set that is a proper subset of

Prove that every convergent sequence is bounded.

In your own words, what does the Nested Interval Property mean and what axiom does it rely on in its proof?

A subset of that contains its supremum but not its infimum.

A sequence such that

Let be the greatest integer less than or equal to . For example,

A function

 \\                =o)  (o>               /\\ _(()__Expressions__\_V_ //                 \\                      \\

For the given code below, which lines are valid (will compile and run)? Assume each line is run independently.   public class Bottle {     private static boolean plastic;     private char letter;     public static int trash() {        return 0;     }     public boolean recycle() {        return true;     }     public static void main(String[] args) {         Bottle obj = new Bottle();         1 obj.recycle();        2 obj.trash();        3 Bottle.recycle();        4 Bottle.trash();                                  5 System.out.println(obj.letter);          6 System.out.println(obj.plastic);        7 System.out.println(Bottle.letter);        8 System.out.println(Bottle.plastic); } }   1  : [1]   2  : [2]   3  : [3]   4  : [4]   5  : [5]   6  : [6]   7  : [7]   8  : [8]