5 ms·
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 se
by 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 agoMaybe we could just define "infinity = 999999" or something like that ...
- gloob 17y agoMaybe 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 agoOne of my favorite pranks on Squeak was to do "true := false" in a workspace window. Sadly, it no longer works...
- leadnose 17y agoI've actually seen that kind of definition in the source of one game.
- calcnerd256 17y agoWhat 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 agohttp://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 agoWhen 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 agoYeah ... 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.)