How to implement infinity in Java?

double supports Infinity

double inf = Double.POSITIVE_INFINITY;
System.out.println(inf + 5);
System.out.println(inf - inf); // same as Double.NaN
System.out.println(inf * -1); // same as Double.NEGATIVE_INFINITY

prints

Infinity
NaN
-Infinity

note: Infinity - Infinity is Not A Number.

I'm supposing you're using integer math for a reason. If so, you can get a result that's functionally nearly the same as POSITIVE_INFINITY by using the MAX_VALUE field of the Integer class:

Integer myInf = Integer.MAX_VALUE;

(And for NEGATIVE_INFINITY you could use MIN_VALUE.) There will of course be some functional differences, e.g., when comparing myInf to a value that happens to be MAX_VALUE: clearly this number isn't less than myInf. Also, as noted in the comments below, incrementing positive infinity will wrap you back around to negative numbers (and decrementing negative infinity will wrap you back to positive).

There's also a library that actually has fields POSITIVE_INFINITY and NEGATIVE_INFINITY, but they are really just new names for MAX_VALUE and MIN_VALUE.

To use Infinity, you can use Double which supports Infinity: -

    System.out.println(Double.POSITIVE_INFINITY);
    System.out.println(Double.POSITIVE_INFINITY * -1);
    System.out.println(Double.NEGATIVE_INFINITY);

    System.out.println(Double.POSITIVE_INFINITY - Double.NEGATIVE_INFINITY);
    System.out.println(Double.POSITIVE_INFINITY - Double.POSITIVE_INFINITY);

OUTPUT: -

Infinity
-Infinity
-Infinity

Infinity 
NaN

The Double and Float types have the POSITIVE_INFINITY constant.

Integer Infinity :

  Integer maxNumber = Integer.MAX_VALUE

Double Infinity

  Double maxNumber = Double.MAX_VALUE;
  Double positiveInf = Double.POSITIVE_INFINITY;
  Double negativeInf = Double.NEGATIVE_INFINITY

Float infinity

   Float positiveInf = Float.POSITIVE_INFINITY;
   Float negativeInf = Float.NEGATIVE_INFINITY
   Float maxNumber = Float.MAX_VALUE;

I'm not sure that Java has infinity for every numerical type but for some numerical data types the answer is positive:

Float.POSITIVE_INFINITY
Float.NEGATIVE_INFINITY

or

Double.POSITIVE_INFINITY
Double.NEGATIVE_INFINITY

Also you may find useful the following article which represents some mathematical operations involving +/- infinity: Java Floating-Point Number Intricacies.

Only Double and Float type support POSITIVE_INFINITY constant.

A generic solution is to introduce a new type. It may be more involved, but it has the advantage of working for any type that doesn't define its own infinity.

If T is a type for which lteq is defined, you can define InfiniteOr<T> with lteq something like this:

class InfiniteOr with type parameter T:
    field the_T of type null-or-an-actual-T
    isInfinite()
        return this.the_T == null
    getFinite():
        assert(!isInfinite());
        return this.the_T
    lteq(that)
        if that.isInfinite()
            return true
        if this.isInfinite()
            return false
        return this.getFinite().lteq(that.getFinite())

I'll leave it to you to translate this to exact Java syntax. I hope the ideas are clear; but let me spell them out anyways.

The idea is to create a new type which has all the same values as some already existing type, plus one special value which—as far as you can tell through public methods—acts exactly the way you want infinity to act, e.g. it's greater than anything else. I'm using null to represent infinity here, since that seems the most straightforward in Java.

If you want to add arithmetic operations, decide what they should do, then implement that. It's probably simplest if you handle the infinite cases first, then reuse the existing operations on finite values of the original type.

There might or might not be a general pattern to whether or not it's beneficial to adopt a convention of handling left-hand-side infinities before right-hand-side infinities or vice versa; I can't tell without trying it out, but for less-than-or-equal (lteq) I think it's simpler to look at right-hand-side infinity first. I note that lteq is not commutative, but add and mul are; maybe that is relevant.

Note: coming up with a good definition of what should happen on infinite values is not always easy. It is for comparison, addition and multiplication, but maybe not subtraction. Also, there is a distinction between infinite cardinal and ordinal numbers which you may want to pay attention to.

For the numeric wrapper types.

e.g Double.POSITIVE_INFINITY

Hope this might help you.

Since the class Number is not final, here is an idea, that I don't find yet in the other posts. Namely to subclass the class Number.

This would somehow deliver an object that can be treated as infinity for Integer, Long, Double, Float, BigInteger and BigDecimal.

Since there are only two values, we could use the singleton pattern:

public final class Infinity extends Number {
    public final static Infinity POSITIVE = new Infinity(false);
    public final static Infinity NEGATIVE = new Infinity(true);
    private boolean negative;
    private Infinity(boolean n) {
        negative = n;
    }
}

Somehow I think the remaining methods intValue(), longValue() etc.. should then be overriden to throw an exceptions. So that the infinity value cannot be used without further precautions.

I'm a beginner in Java... I found another implementation for the infinity in the Java documentation, for the boolean and double types. https://docs.oracle.com/javase/specs/jls/se7/html/jls-4.html#jls-4.2.3

Positive zero and negative zero compare equal; thus the result of the expression 0.0==-0.0 is true and the result of 0.0>-0.0 is false. But other operations can distinguish positive and negative zero; for example, 1.0/0.0 has the value positive infinity, while the value of 1.0/-0.0 is negative infinity.

It looks ugly, but it works.

public class Main {

    public static void main(String[] args) {
        System.out.println(1.0/0.0);
        System.out.println(-1.0/0.0);
    }

}