Re: Mathematical set operations in Java / searching for library

Daniel Pitts <>
Sat, 10 Nov 2007 10:39:58 -0800
Stefan Ram wrote: writes:

thanks. i'm not quite sure, but is it possible to define for
example all natural numbers easily with enumset/set?!

  The set of all Java Integer objects (just written - never
  compiled, so there will still be errors, but you get the idea):

class Integers extends java.util.AbstractSet implements java.util.Set
{ public Integers(){} @java.lang.Override
  public void clear(){ throw new java.lang.UnsupportedOperationException; }
  @java.lang.Override public boolean contains( final java.lang.Object key )
  { return java.lang.Integer.class.isAssignableFrom( key.getClass()); }
  @java.lang.Override public boolean remove( final java.lang.Object key )
  { throw new java.lang.UnsupportedOperationException; }
  @java.lang.Override public int size()
  { return java.lang.Integer.MAX_VALUE; }
  @java.lang.Override public boolean add( final java.lang.Object arg0 )
  { throw new java.lang.UnsupportedOperationException; }
  @java.lang.Override public java.util.Iterator iterator()
  { return new java.util.Iterator()
    { int i = java.lang.Integer.MIN_VALUE;
      public boolean hasNext(){ return i + 1 > i; }
      public java.lang.Object next(){ return ++i; } public void remove()
      { throw new java.lang.UnsupportedOperationException; }}}}

  Mathematical integers can not all be represented as distinct
  objects or values by a computer, because they are not limited
  in size, so a storage for a single mathematical integer value
  would need to have more states the possible different states
  of our whole universe. This also holds for storages of sets of
  mathematical integers.

While the statement is true, the representation of infinite sets can be
accomplished in finite space. You only need to abstract the behavior of
such a set.

For instance, setOfPrimes.intersect(setOfEvenNumbers) would be equal to
the set that contains "2".

While, I wouldn't want to write the implementation of those objects, it
is a feasible undertaking if you add appropriate restrictions on the
number of different types of sets you could do.

Also, if you can create a formula to iterate or calculate certain
properties of the set, then you needn't represent all the values in the set.

in setOfEvenNumbers:
public boolean contains(Integer o) {
    return o.intValue() % 2 == 0;

You might build an abstract interface to mathematical sets that is
different than the Java "Set" interface, as generally in Mathematics,
you specify rules, conditions, relationships, etc. for inclusion in a
set, rather than adding individual elements. Java Collections are very
specifically designed to "hold" collections of Java Objects, not
mathematical abstractions.

There may or may not be such a library already created. I would google
for it before discounting the possibility.

Good luck,

Daniel Pitts' Tech Blog: <>

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