What do these three special floating-point values mean: positive infinity, negative infinity, NaN?

Question

How can we use them in our codes, and what will cause NaN(not a number)?

Answer 1

• Positive infinity means going to infinity in the positive direction -- going into values that are larger and larger in magnitude in the positive direction.
• Negative infinity means going to infinity in the negative direction -- going into values that are larger and larger in magnitude in the negative direction.
• Not-a-number (NaN) is something that is undefined, such as the result of 0/0.

And the constants from the specification of the Float class:

• Float.NEGATIVE_INFINITY
• Float.POSITIVE_INFINITY
• Float.NaN

More information can be found in the IEEE-754 page in Wikipedia.

Here's a little program to illustrate the three constants:

System.out.println(0f / 0f);
System.out.println(1f / 0f);
System.out.println(-1f / 0f);

Output:

NaN
Infinity
-Infinity

Answer 2

This may be a good reference if you want to learn more about floating point numbers in Java.

Positive Infinity is a positive number so large that it can't be represented normally. Negative Infinity is a negative number so large that it cannot be represented normally. NaN means "Not a Number" and results from a mathematical operation that doesn't yield a number- like dividing 0 by 0.

In Java, the Double and Float classes both have constants to represent all three cases. They are POSITIVE_INFINITY, NEGATIVE_INFINITY, and NaN.

Plus consider this:

double a = Math.pow(10, 600) - Math.pow(10, 600); //==NaN

Mathematically, everybody can see it is 0. But for the machine, it is an "Infinity" - "Infinity" (of same Rank), which is indeed NaN.