division by zero: is it really undefined?!
Author
what about the square-root of -1? we gave that an ''i''? This has had me for awhile? What makes one even slightly more rational than another?
It''s generally treated as infinity, but in some cases, it will be something else. It isn''t really undefined. It''s just undefined in computer terms because there is no way to represent infinity (yet?).
In java it just wrights the word "infinity" which sometimes has odd results...
EDIT: At least I think it does, not entirely sure.
-~-The Cow of Darkness-~-
[edited by - cowsarenotevil on April 22, 2003 11:17:57 PM]
EDIT: At least I think it does, not entirely sure.
-~-The Cow of Darkness-~-
[edited by - cowsarenotevil on April 22, 2003 11:17:57 PM]
Because you could have 0/0, which could be any real (or, i suppose, imaginary) value, depending on what function you''re trying to evaluate. Best way to define divide by zero is a limit:
f(x) = a(x)/b(x);
a(p) = b(p) = 0; for some p. So what is f(p)?
Define f(p) = lim (x->p) f(x)
This might also be unbounded in either direction.
Tom
f(x) = a(x)/b(x);
a(p) = b(p) = 0; for some p. So what is f(p)?
Define f(p) = lim (x->p) f(x)
This might also be unbounded in either direction.
Tom
1 / 0 is greater than infinity... because no matter how many times you multiply by 0 its always 0.
If 0/0 had a definition, I could prove that 2 == 1.
Meanwhile, if sqrt(-1) had a definition, I could prove that you can make bass and treble controls for a stereo.
0/0 isn''t defined, even to the limit. Look at these formulas:
1/x == ? when x goes from 1 to 0, this will go from 1 towards positive infinity.
1/x == ? when x goes from -1 to 0, this will go from -1 towards negative infinity.
sin x / x == ? when x goes from either 1 to 0 or -1 to 0, this will go towards 1.
Clearly, something cannot be defined to be valued both -oo, +oo and 1 at the same time.
Meanwhile, if sqrt(-1) had a definition, I could prove that you can make bass and treble controls for a stereo.
0/0 isn''t defined, even to the limit. Look at these formulas:
1/x == ? when x goes from 1 to 0, this will go from 1 towards positive infinity.
1/x == ? when x goes from -1 to 0, this will go from -1 towards negative infinity.
sin x / x == ? when x goes from either 1 to 0 or -1 to 0, this will go towards 1.
Clearly, something cannot be defined to be valued both -oo, +oo and 1 at the same time.
quote:Original post by Cold_SteelJust a comment here. The only math processors I''m really familiar with are the MC6888x family. They have an infinity flag that can be raised under some circumstanses, but division by zero was yet undefined/illegal.
It''s generally treated as infinity, but in some cases, it will be something else. It isn''t really undefined. It''s just undefined in computer terms because there is no way to represent infinity (yet?).
if you just want to work with square roots of negative numbers, do it with complex numbers, not with reals... reals are for newbies 
quote:Original post by CWizard
Just a comment here. The only math processors I''m really familiar with are the MC6888x family. They have an infinity flag that can be raised under some circumstanses, but division by zero was yet undefined/illegal.
That''s true, I forgot about that. I was just thinking that there was no way to represent infinity in an integer format or something like that. IEEE floats do have an overflow or something if I recall correctly, which can be treated as infinity.
Like I said, something divided by zero can have a bunch of different meanings. You guys are right in saying that it is undefined in some situations, but not in all.
Off topic- Hmmm, if we live in a closed universe, would infinity and negative infinity possibly be the same anyway? Food for thought.
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