4 ms·

Is there anything that can do infinity - (infinity-1)?

by teeja 17y ago

bdr 17y ago
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).
- Evgeny 17y ago
  Maybe we could just define "infinity = 999999" or something like that ...
  - gloob 17y ago
    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.
    - rbanffy 17y ago
      One of my favorite pranks on Squeak was to do "true := false" in a workspace window. Sadly, it no longer works...
  - leadnose 17y ago
    I've actually seen that kind of definition in the source of one game.
- calcnerd256 17y ago
  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?
  - modeless 17y ago
    http://www.wolframalpha.com/input/?i=limit+of+x+-+(x+-+1)+as+x+-%3E+infinity http://www.wolframalpha.com/input/?i=limit+of+x+-+(x+-+1)+as... Also, http://www.wolframalpha.com/input/?i=infinity+-+(infinity+-+1) 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.
    - calcnerd256 17y ago
      When I asked it to show its work, it demonstrated that it did the algebra first. I was asking if that's legal here.
- teeja 17y ago
  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.)

Is there anything that can do infinity - (infinity-1)?

by teeja 17y ago

Is there anything that can do infinity - (infinity-1)?

bdr 17y ago

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).

Evgeny 17y ago
Maybe we could just define "infinity = 999999" or something like that ...
- gloob 17y ago
  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.
  - rbanffy 17y ago
    One of my favorite pranks on Squeak was to do "true := false" in a workspace window. Sadly, it no longer works...
- leadnose 17y ago
  I've actually seen that kind of definition in the source of one game.
calcnerd256 17y ago
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?
- modeless 17y ago
  http://www.wolframalpha.com/input/?i=limit+of+x+-+(x+-+1)+as+x+-%3E+infinity http://www.wolframalpha.com/input/?i=limit+of+x+-+(x+-+1)+as... Also, http://www.wolframalpha.com/input/?i=infinity+-+(infinity+-+1) 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.
  - calcnerd256 17y ago
    When I asked it to show its work, it demonstrated that it did the algebra first. I was asking if that's legal here.
teeja 17y ago
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.)