Is Double.POSITIVE_INFINITY a true representation of infinity?

Question

I was wondering if Java's 'Double.POSITIVE_INFINITY' is a true representation of infinity and, if not, will 'i' from this code:

public class Infinity {
private static int i;

public static void main(String[] args) {
    double inf = Double.POSITIVE_INFINITY;
    for (i = 0; i < inf; i++) {
      }
    System.out.println(i);
   }
}

Ever be printed?

Answer 1

Even if you change your code to

double inf = Double.POSITIVE_INFINITY;
for (double i = 0.0; i < inf; i++) {
}
System.out.println(i);

The loop will never end, since i can never become larger than Double.MAX_VALUE, and Double.MAX_VALUE is still smaller than Double.POSITIVE_INFINITY.

You can prove it by running this snippet:

if (Double.MAX_VALUE > Double.POSITIVE_INFINITY) {
  System.out.println ("max is larger than infinity");
} else {
  System.out.println ("nope");
}

which will print "nope", since Double.POSITIVE_INFINITY is larger than any possible double value. BTW, the compiler marks the System.out.println ("max is larger than infinity"); statement as dead code.

I guess this means you could say 'Double.POSITIVE_INFINITY' is a true representation of infinity.

BTW, the value of POSITIVE_INFINITY is

public static final double POSITIVE_INFINITY = 1.0 / 0.0;

Therefore, since 1.0/0.0 is actually positive infinity, you can say it's a true representation of infinity.