Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Topic: adding irrational numbers
Replies: 14   Last Post: Oct 10, 2012 3:13 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 467
From: ct
Registered: 6/14/08
Re: adding irrational numbers
Posted: Oct 10, 2012 3:13 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

> Let i1 = .010010001000010000010000001...
> and i2 = .101101110111101111101111110...
> Clearly both of these non-repeating decimals
> are irrational, and their
> sum i3 = .111111111111111111111111111...
> which is repeating, rational, and = 1/9
> One could easily make up numerous examples
> similar to this one of pairs of irrationals whose
> sum is rational, and others whose sum is
> irrational.
> Note that in the above case the sum is arrived
> at by simple intuition, not by any procedure of
> addition.
> questions:
> 1) Has there been any notable work done in this area?
> 2) Are there any known examples of irrationals not
> made up in this way which have rational sums?
> 3) Is there any theory of a method of adding
> irrational numbers other than the intuitive approach
> indicated above, which obviously is severely limited
> in scope?

The 9's compliment comes to mind --
The 9's compliment of pi is irrational
and = 6.8584073464102067... + pi =
9.999999999... = 10
This will happen with any irrational.


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum 1994-2015. All Rights Reserved.