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A sequence such that

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

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]

You have a file Cat.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) {         Cat t = new Cat();         // each of the lines below is run independently        System.out.println(t.age);    // compiles and runs        System.out.println(t.isKitten); // compiles and runs System.out.println(t.getIsKitten()); // compile error     } }  —— in a separate file in a different package/directory ———  public class Cat {        1   int age;       2   boolean isKitten;       3   boolean getIsKitten() {        return isKitten;     }     /** no-argument constructor implemented **/ }    1  :[vis1]   2  :[vis2]   3  :[vis3]

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Complete the following code. Make sure to complete the code in such a way that doesn’t invalidate the comments and that no implicit conversions are taking place on assignments of primitive data types.  [import] public class Test {     public static void main(String[] args) {         int percent;         double price;         // create a keyboard Scanner         Scanner scanner = [init]         // get an integer value from the user         percent = [int]          // get a double value from the user         price = [double]           // compute sale         double sale = price * (percent/100.00);         // print sale to 1 decimal place    [print]     } }