Re:999999999999999 - 999999999999997
by bdr on Monday August 24, 2009 @06:23PM
(#783553)
Even in non-standard models of arithmetic, where you could use infinity as an operand, the value of that expression would have to be undefined (not 1, as you seem to expect).
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Yeah ... I was suggesting that a more sophisticated algorithm for arithmetic on very large integers could eliminate substantial similarities, leaving the 'zone of difference'. A limited 'bit window' needs to be more versatile.
For example, a while back a man got a bill for $35 billion ... that wouldn't happen with more intelligence built into routines. (OUR minds look at 999...999 and 999...997 and see quickly what can be eliminated.)
Re:999999999999999 - 999999999999997
by calcnerd256 on Monday August 24, 2009 @07:20PM
(#783650)
What about limit as x goes to infinity of x - (x - 1)? We do the algebra first, right? Now, that's a special case of y - (x - 1) where y = x, so can we get a different residue by going about the limit in two dimensions?
http://www.wolframalpha.com/input/?i=limit+of+x+-+(x+-+1)+as...
Also, http://www.wolframalpha.com/input/?i=infinity+-+(infinity+-+...
If nothing else, Wolfram Alpha is useful for math. I'm impressed that it understood my syntax for limits that I made up on the spot, first try.
Re:999999999999999 - 999999999999997
by calcnerd256 on Thursday August 27, 2009 @11:29PM
(#790685)
When I asked it to show its work, it demonstrated that it did the algebra first. I was asking if that's legal here.
Maybe we could just define "infinity = 999999" or something like that ...
Maybe we could just define "zero = 123456789" or something like that while we're at it. If we're going to break math we may as well go whole hog.
One of my favorite pranks on Squeak was to do "true := false" in a workspace window.
Sadly, it no longer works...