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Ask Slashdot: What's the Harm In a Default Setting For Div By Zero?
New submitter CodeInspired writes: After 20 years of programming, I've decided I'm tired of checking for div by zero. Would there be any serious harm in allowing a system wide setting that said div by zero simply equals zero? Maybe it exists already, not sure. But I run into it all the time in every language I've worked with. Does anyone want their div by zero errors to result in anything other than zero?
Mathematically, the result is undefined. So neither is correct. Nor is anything inbetween.
When you have 0/0, you hit two "obvious" but contradictory rules in basic algebra:
Rule one: anything multiplied by zero is zero
Rule two: anything divided by itself is one
Ugh no, just no.
"Rule one: anything multiplied by zero is zero"
Yes, this is called, amongst other things, the zero property of multiplication. However 0/0 is not a multiplication and the rule is not relevant, and there is no conflict.
Secondly your "rule two" is not actually rule of algebra. There is no rule x/x = 1.
There is an identity rule for division: anything divided by one is itself (x/1 = x) but there is no rule that says x/x = 1
You can derive "rule two" from the identity rule for multiplication x*1 = x --> x/x = 1
However, that transformation always stipulates that x 0 because division by zero is undefined.
Mathematicians have no issue determine which rule has precedence, because neither rule applies to 0/0.
There is no conflict. Division by zero is specifically "undefined".
Consider the equation; x/x.
http://www.wolframalpha.com/in...
The graph of the function is a horizontal line at y=1, with a discontinuity at 0. (if x=0, x/x=0/0) So 0/0 should be 1 right? Because everywhere else on the graph x/x = 1??
http://www.wolframalpha.com/in...
Now consider the equation 2x/x.
http://www.wolframalpha.com/in...
As x approaches 0 (lim x->0) from either the left or right the limit of the equation is 2. A graph of the function is horizontal line at y=2, with a discontinuity at 0. But every where else 2x/x = 2. So shouldn't 2(0)/0 = 0/0 = 2? So 0/0 should be 2 right?
http://www.wolframalpha.com/in...
Neither. Its not defined.
Now consider the equation 1/x.
http://www.wolframalpha.com/in...
As x approaches 0 from the left it goes to negative infinity. As x approaches 0 from the right it goes to positive infinity. This graph doesn't even suggest a value for 0/0? Is it + infinity? Or - infinity?
I can write a function that makes 0/0 look like it should be anything I want.
0/0 is undefined. It doesn't violate any rules of algebra. It's a rule of algebra that division by 0 is undefined.