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

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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]

You have a file Chocolate.java and you have a driver class named Driver.java. Fill in the correct visibility modifiers so that the comments in the main method are upheld.  public class Driver {     public static void main(String[] args) {         Chocolate t = new Chocolate();         // each of the lines below is run independently        System.out.println(t.numPieces); // compile error         System.out.println(t.getCost()); // compiles and runs        System.out.println(t.cost); // compiles and runs     } } —— in a separate file in a different package/directory ———  public class Chocolate {        1   int numPieces;       2   double cost;       3   double getCost() {        return cost;     }     /** no-argument constructor implemented **/ }    1  :[vis1]   2  :[vis2]   3  :[vis3]