The + symbol can mean three distinct operators in Java:

• If there is no operand before the +, then it is the unary Plus operator.
• If there are two operands, and they are both numeric. then it is the binary Addition operator.
• If there are two operands, and at least one of them is a String, then it it the binary Concatenation operator.

In the simple case, the Concatenation operator joins two strings to give a third string. For example:

String s1 = "a String";
String s2 = "This is " + s1;    // s2 contains "This is a String"

When one of the two operands is not a string, it is converted to a String as follows:

• An operand whose type is a primitive type is converted as if by calling toString() on the boxed value.

• An operand whose type is a reference type is converted by calling the operand's toString() method. If the operand is null, or if the toString() method returns null, then the string literal "null" is used instead.

For example:

int one = 1;
String s3 = "One is "  + one;         // s3 contains "One is 1"
String s4 = null + " is null";        // s4 contains "null is null"
String s5 = "{1} is " + new int[]{1}; // s5 contains something like
                                      // "{} is [I@xxxxxxxx"

The explanation for the s5 example is that the toString() method on array types is inherited from java.lang.Object, and the behavior is to produce a string that consists of the type name, and the object's identity hashcode.

The Concatenation operator is specified to create a new String object, except in the case where the expression is a Constant Expression. In the latter case, the expression is evaluated at compile type, and its runtime value is equivalent to a string literal. This means that there is no runtime overhead in splitting a long string literal like this:

String typing = "The quick brown fox " +
                "jumped over the " +
                "lazy dog";           // constant expression

Optimization and efficiency

As noted above, with the exception of constant expressions, each string concatenation expression creates a new String object. Consider this code:

public String stars(int count) {
    String res = "";
    for (int i = 0; i < count; i++) {
        res = res + "*";
    }
    return res;
}

In the method above, each iteration of the loop will create a new String that is one character longer than the previous iteration. Each concatenation copies all of the characters in the operand strings to form the new String. Thus, stars(N) will:

• create N new String objects, and throw away all but the last one,
• copy N * (N + 1) / 2 characters, and
• generate O(N^2) bytes of garbage.

This is very expensive for large N. Indeed, any code that concatenates strings in a loop is liable to have this problem. A better way to write this would be as follows:

public String stars(int count) {
    // Create a string builder with capacity 'count' 
    StringBuilder sb = new StringBuilder(count);
    for (int i = 0; i < count; i++) {
        sb.append("*");
    }
    return sb.toString();
}

Ideally, you should set the capacity of the StringBuilder, but if this is not practical, the class will automatically grow the backing array that the builder uses to hold characters. (Note: the implementation expands the backing array exponentially. This strategy keeps that amount of character copying to a O(N) rather than O(N^2).)

Some people apply this pattern to all string concatenations. However, this is unnecessary because the JLS allows a Java compiler to optimize string concatenations within a single expression. For example:

String s1 = ...;
String s2 = ...;    
String test = "Hello " + s1 + ". Welcome to " + s2 + "\n";

will typically be optimized by the bytecode compiler to something like this;

StringBuilder tmp = new StringBuilder();
tmp.append("Hello ")
tmp.append(s1 == null ? "null" + s1);
tmp.append("Welcome to ");
tmp.append(s2 == null ? "null" + s2);
tmp.append("\n");
String test = tmp.toString();

(The JIT compiler may optimize that further if it can deduce that s1 or s2 cannot be null.) But note that this optimization is only permitted within a single expression.

In short, if you are concerned about the efficiency of string concatenations:

• Do hand-optimize if you are doing repeated concatenation in a loop (or similar).
• Don't hand-optimize a single concatenation expression.

The Java language provides 7 operators that perform arithmetic on integer and floating point values.

• There are two + operators:
  • The binary addition operator adds one number to another one. (There is also a binary + operator that performs string concatenation. That is described in a separate example.)
  • The unary plus operator does nothing apart from triggering numeric promotion (see below)
• There are two - operators:
  • The binary subtraction operator subtracts one number from another one.
  • The unary minus operator is equivalent to subtracting its operand from zero.
• The binary multiply operator (*) multiplies one number by another.
• The binary divide operator (/) divides one number by another.
• The binary remainder¹ operator (%) calculates the remainder when one number is divided by another.

^{1. This is often incorrectly referred to as the "modulus" operator. "Remainder" is the term that is used by the JLS. "Modulus" and "remainder" are not the same thing.}

Operand and result types, and numeric promotion

The operators require numeric operands and produce numeric results. The operand types can be any primitive numeric type (i.e. byte, short, char, int, long, float or double) or any numeric wrapper type define in java.lang; i.e. (Byte, Character, Short, Integer, Long, Float or Double.

The result type is determined base on the types of the operand or operands, as follows:

• If either of the operands is a double or Double, then the result type is double.
• Otherwise, if either of the operands is a float or Float, then the result type is float.
• Otherwise, if either of the operands is a long or Long, then the result type is long.
• Otherwise, the result type is int. This covers byte, short and char operands as well as `int.

The result type of the operation determines how the arithmetic operation is performed, and how the operands are handled

• If the result type is double, the operands are promoted to double, and the operation is performed using 64-bit (double precision binary) IEE 754 floating point arithmetic.
• If the result type is float, the operands are promoted to float, and the operation is performed using 32-bit (single precision binary) IEE 754 floating point arithmetic.
• If the result type is long, the operands are promoted to long, and the operation is performed using 64-bit signed twos-complement binary integer arithmetic.
• If the result type is int, the operands are promoted to int, and the operation is performed using 32-bit signed twos-complement binary integer arithmetic.

Promotion is performed in two stages:

• If the operand type is a wrapper type, the operand value is unboxed to a value of the corresponding primitive type.
• If necessary, the primitive type is promoted to the required type:
  • Promotion of integers to int or long is loss-less.
  • Promotion of float to double is loss-less.
  • Promotion of an integer to a floating point value can lead to loss of precision. The conversion is performed using IEE 768 "round-to-nearest" semantics.

The meaning of division

The / operator divides the left-hand operand n (the dividend) and the right-hand operand d (the divisor) and produces the result q (the quotient).

Java integer division rounds towards zero. The JLS Section 15.17.2 specifies the behavior of Java integer division as follows:

The quotient produced for operands n and d is an integer value q whose magnitude is as large as possible while satisfying |d ⋅ q| ≤ |n|. Moreover, q is positive when |n| ≥ |d| and n and d have the same sign, but q is negative when |n| ≥ |d| and n and d have opposite signs.

There are a couple of special cases:

• If the n is MIN_VALUE, and the divisor is -1, then integer overflow occurs and the result is MIN_VALUE. No exception is thrown in this case.
• If d is 0, then `ArithmeticException is thrown.

Java floating point division has more edge cases to consider. However the basic idea is that the result q is the value that is closest to satisfying d . q = n.

Floating point division will never result in an exception. Instead, operations that divide by zero result in an INF and NaN values; see below.

The meaning of remainder

Unlike C and C++, the remainder operator in Java works with both integer and floating point operations.

For integer cases, the result of a % b is defined to be the number r such that (a / b) * b + r is equal to a, where /, * and + are the appropriate Java integer operators. This applies in all cases except when b is zero. That case, remainder results in an ArithmeticException.

It follows from the above definition that a % b can be negative only if a is negative, and it be positive only if a is positive. Moreover, the magnitude of a % b is always less than the magnitude of b.

Floating point remainder operation is a generalization of the integer case. The result of a % b is the remainder r is defined by the mathematical relation r = a - (b ⋅ q) where:

• q is an integer,
• it is negative only if a / b is negative an positive only if a / b is positive, and
• its magnitude is as large as possible without exceeding the magnitude of the true mathematical quotient of a and b.

Floating point remainder can produce INF and NaN values in edge-cases such as when b is zero; see below. It will not throw an exception.

Important note:

The result of a floating-point remainder operation as computed by % is not the same as that produced by the remainder operation defined by IEEE 754. The IEEE 754 remainder may be computed using the Math.IEEEremainder library method.

Integer Overflow

Java 32 and 64 bit integer values are signed and use twos-complement binary representation. For example, the range of numbers representable as (32 bit) int -2³¹ through +2³¹ - 1.

When you add, subtract or multiple two N bit integers (N == 32 or 64), the result of the operation may be too large to represent as an N bit integer. In this case, the operation leads to integer overflow, and the result can be computed as follows:

• The mathematical operation is performed to give a intermediate two's-complement representation of the entire number. This representation will be larger than N bits.
• The bottom 32 or 64 bits of the intermediate representation are used as the result.

It should be noted that integer overflow does not result in exceptions under any circumstances.

Floating point INF and NAN values

Java uses IEE 754 floating point representations for float and double. These representations have some special values for representing values that fall outside of the domain of Real numbers:

• The "infinite" or INF values denote numbers that are too large. The +INF value denote numbers that are too large and positive. The -INF value denote numbers that are too large and negative.
• The "indefinite" / "not a number" or NaN denote values resulting from meaningless operations.

The INF values are produced by floating operations that cause overflow, or by division by zero.

The NaN values are produced by dividing zero by zero, or computing zero remainder zero.

Surprisingly, it is possible perform arithmetic using INF and NaN operands without triggering exceptions. For example:

• Adding +INF and a finite value gives +INF.
• Adding +INF and +INF gives +INF.
• Adding +INF and -INF gives NaN.
• Dividing by INF gives either +0.0 or -0.0.
• All operations with one or more NaN operands give NaN.

For full details, please refer to the relevant subsections of JLS 15. Note that this is largely "academic". For typical calculations, an INF or NaN means that something has gone wrong; e.g. you have incomplete or incorrect input data, or the calculation has been programmed incorrectly.

The == and != operators are binary operators that evaluate to true or false depending on whether the operands are equal. The == operator gives true if the operands are equal and false otherwise. The != operator gives false if the operands are equal and true otherwise.

These operators can be used operands with primitive and reference types, but the behavior is significantly different. According to the JLS, there are actually three distinct sets of these operators:

• The Boolean == and != operators.
• The Numeric == and != operators.
• The Reference == and != operators.

However, in all cases, the result type of the == and != operators is boolean.

The Numeric == and != operators

When one (or both) of the operands of an == or != operator is a primitive numeric type (byte, short, char, int, long, float or double), the operator is a numeric comparison. The second operand must be either a primitive numeric type, or a boxed numeric type.

The behavior other numeric operators is as follows:

1. If one of the operands is a boxed type, it is unboxed.
2. If either of the operands now a byte, short or char, it is promoted to an int.
3. If the types of the operands are not the same, then the operand with the "smaller" type is promoted to the "larger" type.
4. The comparison is then carried out as follows:
   • If the promoted operands are int or long then the values are tested to see if they are identical.
   • If the promoted operands are float or double then:
     • the two versions of zero (+0.0 and -0.0) are treated as equal
     • a NaN value is treated as not equals to anything, and
     • other values are equal if their IEEE 754 representations are identical.

Note: you need to be careful when using == and != to compare floating point values.

The Boolean == and != operators

If both operands are boolean, or one is boolean and the other is Boolean, these operators the Boolean == and != operators. The behavior is as follows:

1. If one of the operands is a Boolean, it is unboxed.
2. The unboxed operands are tested and the boolean result is calculated according to the following truth table

There are two "pitfalls" that make it advisable to use == and != sparingly with truth values:

• If you use == or != to compare two Boolean objects, then the Reference operators are used. This may give an unexpected result; see Pitfall: using == to compare primitive wrappers objects such as Integer

• The == operator can easily be mistyped as =. For most operand types, this mistake leads to a compilation error. However, for boolean and Boolean operands the mistake leads to incorrect runtime behavior; see Pitfall - Using '==' to test a boolean

The Reference == and != operators

If both operands are object references, the == and != operators test if the two operands refer to the same object. This often not what you want. To test if two objects are equal by value, the .equals() method should be used instead.

String s1 = "We are equal";
String s2 = new String("We are equal");

s1.equals(s2); // true

// WARNING - don't use == or != with String values
s1 == s2;      // false

Warning: using == and != to compare String values is incorrect in most cases; see http://stackoverflow.com/documentation/java/4388/java-pitfalls/16290/using-to-compare-strings . A similar problem applies to primitive wrapper types; see http://stackoverflow.com/documentation/java/4388/java-pitfalls/8996/using-to-compare-primitive-wrappers-objects-such-as-integer .

About the NaN edge-cases

JLS 15.21.1 states the following:

If either operand is NaN, then the result of == is false but the result of != is true. Indeed, the test x != x is true if and only if the value of x is NaN.

This behavior is (to most programmers) unexpected. If you test if a NaN value is equal to itself, the answer is "No it isn't!". In other words, == is not reflexive for NaN values.

However, this is not a Java "oddity", this behavior is specified in the IEEE 754 floating-point standards, and you will find that it is implemented by most modern programming languages. (For more information, see http://stackoverflow.com/a/1573715/139985 ... noting that this is written by someone who was "in the room when the decisions were made"!)

Variables can be incremented or decremented by 1 using the ++ and -- operators, respectively.

When the ++ and -- operators follow variables, they are called post-increment and post-decrement respectively.

int a = 10;
a++; // a now equals 11
a--; // a now equals 10 again

When the ++ and -- operators precede the variables the operations are called pre-increment and pre-decrement respectively.

int x = 10;
--x; // x now equals 9
++x; // x now equals 10

If the operator precedes the variable, the value of the expression is the value of the variable after being incremented or decremented. If the operator follows the variable, the value of the expression is the value of the variable prior to being incremented or decremented.

int x=10;

System.out.println("x=" + x + " x=" + x++ + " x=" + x); // outputs x=10 x=10 x=11
System.out.println("x=" + x + " x=" + ++x + " x=" + x); // outputs x=11 x=12 x=12
System.out.println("x=" + x + " x=" + x-- + " x=" + x); // outputs x=12 x=12 x=11
System.out.println("x=" + x + " x=" + --x + " x=" + x); // outputs x=11 x=10 x=10

Be careful not to overwrite post-increments or decrements. This happens if you use a post-in/decrement operator at the end of an expression which is reassigned to the in/decremented variable itself. The in/decrement will not have an effect. Even though the variable on the left hand side is incremented correctly, its value will be immediately overwritten with the previously evaluated result from the right hand side of the expression:

int x = 0; 
x = x++ + 1 + x++;      // x = 0 + 1 + 1 
                        // do not do this - the last increment has no effect (bug!) 
System.out.println(x);  // prints 2 (not 3!) 

Correct:

int x = 0;
x = x++ + 1 + x;        // evaluates to x = 0 + 1 + 1
x++;                    // adds 1
System.out.println(x);  // prints 3 

Syntax

{condition-to-evaluate} ? {statement-executed-on-true} : {statement-executed-on-false}

As shown in the syntax, the Conditional Operator (also known as the Ternary Operator¹) uses the ? (question mark) and : (colon) characters to enable a conditional expression of two possible outcomes. It can be used to replace longer if-else blocks to return one of two values based on condition.

result = testCondition ? value1 : value2

Is equivalent to

if (testCondition) { 
    result = value1; 
} else { 
    result = value2; 
}

It can be read as “If testCondition is true, set result to value1; otherwise, set result to value2”.

For example:

// get absolute value using conditional operator 
a = -10;
int absValue = a < 0 ? -a : a;
System.out.println("abs = " + absValue); // prints "abs = 10"

Is equivalent to

// get absolute value using if/else loop
a = -10;
int absValue;
if (a < 0) {
    absValue = -a;
} else {
    absValue = a;
}
System.out.println("abs = " + absValue); // prints "abs = 10"

Common Usage

You can use the conditional operator for conditional assignments (like null checking).

String x = y != null ? y.toString() : ""; //where y is an object

This example is equivalent to:

String x = "";

if (y != null) {
    x = y.toString();
}

Since the Conditional Operator has the second-lowest precedence, above the Assignment Operators, there is rarely a need for use parenthesis around the condition, but parenthesis is required around the entire Conditional Operator construct when combined with other operators:

// no parenthesis needed for expressions in the 3 parts
10 <= a && a < 19 ? b * 5 : b * 7

// parenthesis required
7 * (a > 0 ? 2 : 5)

Conditional operators nesting can also be done in the third part, where it works more like chaining or like a switch statement.

a ? "a is true" :
b ? "a is false, b is true" :
c ? "a and b are false, c is true" :
    "a, b, and c are false"

//Operator precedence can be illustrated with parenthesis:

a ? x : (b ? y : (c ? z : w))

Footnote:

^{1 - Both the Java Language Specification and the Java Tutorial call the (? :) operator the Conditional Operator. The Tutorial says that it is "also known as the Ternary Operator" as it is (currently) the only ternary operator defined by Java. The "Conditional Operator" terminology is consistent with C and C++ and other languages with an equivalent operator.}

The Java language provides 4 operators that perform bitwise or logical operations on integer or boolean operands.

• The complement (~) operator is a unary operator that performs a bitwise or logical inversion of the bits of one operand; see JLS 15.15.5..
• The AND (&) operator is a binary operator that performs a bitwise or logical "and" of two operands; see JLS 15.22.2..
• The OR (|) operator is a binary operator that performs a bitwise or logical "inclusive or" of two operands; see JLS 15.22.2..
• The XOR (^) operator is a binary operator that performs a bitwise or logical "exclusive or" of two operands; see JLS 15.22.2..

The logical operations performed by these operators when the operands are booleans can be summarized as follows:

Note that for integer operands, the above table describes what happens for individual bits. The operators actually operate on all 32 or 64 bits of the operand or operands in parallel.

Operand types and result types.

The usual arithmetic conversions apply when the operands are integers. Common use-cases for the bitwise operators

The ~ operator is used to reverse a boolean value, or change all the bits in an integer operand.

The & operator is used for "masking out" some of the bits in an integer operand. For example:

int word = 0b00101010;
int mask = 0b00000011;   // Mask for masking out all but the bottom 
                         // two bits of a word
int lowBits = word & mask;            // -> 0b00000010
int highBits = word & ~mask;          // -> 0b00101000

The | operator is used to combine the truth values of two operands. For example:

int word2 = 0b01011111; 
// Combine the bottom 2 bits of word1 with the top 30 bits of word2
int combined = (word & mask) | (word2 & ~mask);   // -> 0b01011110

The ^ operator is used for toggling or "flipping" bits:

int word3 = 0b00101010;
int word4 = word3 ^ mask;             // -> 0b00101001

For more examples of the use of the bitwise operators, see Bit Manipulation

This operator checks whether the object is of a particular class/interface type. instanceof operator is written as:

( Object reference variable ) instanceof  (class/interface type)

Example:

public class Test {

   public static void main(String args[]){
      String name = "Buyya";
      // following will return true since name is type of String
      boolean result = name instanceof String;  
      System.out.println( result );
   }
}

This would produce the following result:

true

This operator will still return true if the object being compared is the assignment compatible with the type on the right.

Example:

class Vehicle {}

public class Car extends Vehicle {
   public static void main(String args[]){
      Vehicle a = new Car();
      boolean result =  a instanceof Car;
      System.out.println( result );
   }
}

This would produce the following result:

true

The left hand operand for these operators must be a either a non-final variable or an element of an array. The right hand operand must be assignment compatible with the left hand operand. This means that either the types must be the same, or the right operand type must be convertible to the left operands type by a combination of boxing, unboxing or widening. (For complete details refer to JLS 5.2.)

The precise meaning of the "operation and assign" operators is specified by JLS 15.26.2 as:

A compound assignment expression of the form E1 op= E2 is equivalent to E1 = (T) ((E1) op (E2)), where T is the type of E1, except that E1 is evaluated only once.

Note that there is an implicit type-cast before the final assignment.

1. =

The simple assignment operator: assigns the value of the right hand operand to the left hand operand.

Example: c = a + b will add the value of a + b to the value of c and assign it to c

2. +=

The "add and assign" operator: adds the value of right hand operand to the value of the left hand operand and assigns the result to left hand operand. If the left hand operand has type String, then this a "concatenate and assign" operator.

Example: c += a is roughly the same as c = c + a

3. -=

The "subtract and assign" operator: subtracts the value of the right operand from the value of the left hand operand and assign the result to left hand operand.

Example: c -= a is roughly the same as c = c - a

4. *=

The "multiply and assign" operator: multiplies the value of the right hand operand by the value of the left hand operand and assign the result to left hand operand. .

Example: c *= a is roughly the same as c = c * a

5. /=

The "divide and assign" operator: divides the value of the right hand operand by the value of the left hand operand and assign the result to left hand operand.

Example: c /*= a is roughly the same as c = c / a

6. %=

The "modulus and assign" operator: calculates the modulus of the value of the right hand operand by the value of the left hand operand and assign the result to left hand operand.

Example: c %*= a is roughly the same as c = c % a

7. <<=

The "left shift and assign" operator.

Example: c <<= 2 is roughly the same as c = c << 2

8. >>=

The "arithmetic right shift and assign" operator.

Example: c >>= 2 is roughly the same as c = c >> 2

9. >>>=

The "logical right shift and assign" operator.

Example: c >>>= 2 is roughly the same as c = c >>> 2

10. &=

The "bitwise and and assign" operator.

Example: c &= 2 is roughly the same as c = c & 2

11. |=

The "bitwise or and assign" operator.

Example: c |= 2 is roughly the same as c = c | 2

12. ^=

The "bitwise exclusive or and assign" operator.

Example: c ^= 2 is roughly the same as c = c ^ 2

Java provides a conditional-and and a conditional-or operator, that both take one or two operands of type boolean and produce a boolean result. These are:

• && - the conditional-AND operator,

• || - the conditional-OR operators. The evaluation of <left-expr> && <right-expr> is equivalent to the following pseudo-code:

  {
     boolean L = evaluate(<left-expr>);
     if (L) {
         return evaluate(<right-expr>);
     } else {
         // short-circuit the evaluation of the 2nd operand expression
         return false;
     }
  }
  

The evaluation of <left-expr> || <right-expr> is equivalent to the following pseudo-code:

    {
       boolean L = evaluate(<left-expr>);
       if (!L) {
           return evaluate(<right-expr>);
       } else {
           // short-circuit the evaluation of the 2nd operand expression
           return true;
       }
    }

As the pseudo-code above illustrates, the behavior of the short-circuit operators are equivalent to using if / else statements.

Example - using && as a guard in an expression

The following example shows the most common usage pattern for the && operator. Compare these two versions of a method to test if a supplied Integer is zero.

public boolean isZero(Integer value) {
    return value == 0;
}

public boolean isZero(Integer value) {
    return value != null && value == 0;
}

The first version works in most cases, but if the value argument is null, then a NullPointerException will be thrown.

In the second version we have added a "guard" test. The value != null && value == 0 expression is evaluated by first performing the value != null test. If the null test succeeds (i.e. it evaluates to true) then the value == 0 expression is evaluated. If the null test fails, then the evaluation of value == 0 is skipped (short-circuited), and we don't get a NullPointerException.

Example - using && to avoid a costly calculation

The following example shows how && can be used to avoid a relatively costly calculation:

public boolean verify(int value, boolean needPrime) {
    return !needPrime | isPrime(value);
}

public boolean verify(int value, boolean needPrime) {
    return !needPrime || isPrime(value);
}

In the first version, both operands of the | will always be evaluated, so the (expensive) isPrime method will be called unnecessarily. The second version avoids the unnecessary call by using || instead of |.

The Java language provides three operator for performing bitwise shifting on 32 and 64 bit integer values. These are all binary operators with the first operand being the value to be shifted, and the second operand saying how far to shift.

• The << or left shift operator shifts the value given by the first operand leftwards by the number of bit positions given by the second operand. The empty positions at the right end are filled with zeros.

• The '>>' or arithmetic shift operator shifts the value given by the first operand rightwards by the number of bit positions given by the second operand. The empty positions at the left end are filled by copying the left-most bit. This process is known as sign extension.

• The '>>>' or logical right shift operator shifts the value given by the first operand rightwards by the number of bit positions given by the second operand. The empty positions at the left end are filled with zeros.

Notes:

1. These operators require an int or long value as the first operand, and produce a value with the same type as the first operand. (You will need to use an explicit type cast when assigning the result of a shift to a byte, short or char variable.)

2. If you use a shift operator with a first operand that is a byte, char or short, it is promoted to an int and the operation produces an int.)

3. The second operand is reduced modulo the number of bits of the operation to give the amount of the shift. For more about the mod mathematical concept, see Modulus examples.

4. The bits that are shifted off the left or right end by the operation are discarded. (Java does not provide a primitive "rotate" operator.)

5. The arithmetic shift operator is equivalent dividing a (two's complement) number by a power of 2.

6. The left shift operator is equivalent multiplying a (two's complement) number by a power of 2.

The following table will help you see the effects of the three shift operators. (The numbers have been expressed in binary notation to aid vizualization.)

There examples of the user of shift operators in Bit manipulation

From Java 8 onwards, the Lambda operator ( -> ) is the operator used to introduce a Lambda Expression. There are two common syntaxes, as illustrated by these examples:

  a -> a + 1              // a lambda that adds one to its argument
  a -> { return a + 1; }  // an equivalent lambda using a block.

A lambda expression defines an anonymous function, or more correctly an instance of an anonymous class that implements a functional interface.

(This example is included here for completeness. Refer to the Lambda Expressions topic for the full treatment.)

The operators <, <=, > and >= are binary operators for comparing numeric types. The meaning of the operators is as you would expect. For example, if a and b are declared as any of byte, short, char, int, long, float, double or the corresponding boxed types:

- `a < b` tests if the value of `a` is less than the value of `b`. 
- `a <= b` tests if the value of `a` is less than or equal to the value of `b`. 
- `a > b` tests if the value of `a` is greater than the value of `b`. 
- `a >= b` tests if the value of `a` is greater than or equal to the value of `b`. 

The result type for these operators is boolean in all cases.

Relational operators can be used to compare numbers with different types. For example:

int i = 1;
long l = 2;
if (i < l) {
    System.out.println("i is smaller");
}

Relational operators can be used when either or both numbers are instances of boxed numeric types. For example:

Integer i = 1;   // 1 is autoboxed to an Integer
Integer j = 2;   // 2 is autoboxed to an Integer
if (i < j) {
    System.out.println("i is smaller");
}

The precise behavior is summarized as follows:

1. If one of the operands is a boxed type, it is unboxed.
2. If either of the operands now a byte, short or char, it is promoted to an int.
3. If the types of the operands are not the same, then the operand with the "smaller" type is promoted to the "larger" type.
4. The comparison is performed on the resulting int, long, float or double values.

You need to be careful with relational comparisons that involve floating point numbers:

• Expressions that compute floating point numbers often incur rounding errors due to the fact that the computer floating-point representations have limited precision.
• When comparing an integer type and a floating point type, the conversion of the integer to floating point can also lead to rounding errors.

Finally, Java does bit support the use of relational operators with any types other than the ones listed above. For example, you cannot use these operators to compare strings, arrays of numbers, and so on.