How to implement infinity in Java

Question

Does Java have anything to represent infinity for every numerical data type  How is it implemented such that I can do mathematical operations with it   E g   int myInf   infinity    However it is done myInf   5    returns infinity myInf  -1     returns negative infinity   I have tried using very large numbers  but I want a proper  easy solution

User · Answer

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

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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 lt T gt  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

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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

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Only Double and Float type support POSITIVE INFINITY constant

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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

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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

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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

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The Double and Float types have the POSITIVE INFINITY constant

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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

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For the numeric wrapper types   e g Double POSITVE INFINITY   Hope this might help you

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