🚀 go-pugleaf

jon murray wrote:
> 
> William Chops Westfield wrote:
> >
> >     Which is the larger set of numbers: All positive integers, or all integers?
> >     Both are infinity, but is one set twice as large as the other?
> >
> > They're the same size.  The set of all rational number (fractions) is
> > the same size too.  But the set of irrational numbers is bigger...
> >
> > That should be obvious.
> >
> 
> Well, not being a mathematitian, it isn't obvious to me. Is there any
> imaginable situation where my lack of insight is likely to cause me a
> problem?
> 

	No, but the explanation is rather simple.

Integers 	1 -1 2 -2 3 -3 4 -4 etc... (This will obviously go to
infinity)
Positive Int	1  2 3  4 5  6 7  8 etc.  (This too will go to infinity).

Basically you can count to infinity with either one.

The reason irrationals are a "bigger" infinity is as follows.

Count from 1 to 2 with every irrational inbetween...

All Number set:   1 1.1 1.11 1.111 1.1111 1.11111 ...... up to 2.
Integers	  1  2   3    4     5      6   up to infinity.

So, (wrap your mind around this :-) you get to infinity with the
integers before you get to 2.  So what happens when you finally get to
2?  You're out of inifite integers, but you've got an inifity to go. :-)

In other words, it takes an infinite number of "counters" to get from
1.0 to 2.0.  So, it must take a BIGGER infinite number of counters to
get from 1.0 to infinity.0.

Make sense?


> Jon
> 
> *********
> My address has been spam-protected.
> It's 'netconnect' & I live in Australia (.au)
> *********

-- 
Greg D. Moore	President  	mooregr@greenms.com
Green Mountain Software		http://www.greenms.com/
518-273-8602