Talk:Detect division by zero

Many of the solutions here simply check that the result is infinite. This will fail if the numerator is 0 too, since 0 / 0 is mathematically incalculable (many languages return NaN here).

A correct pseudocode solution is:

result = numerator / denominator
if numerator equals 0
   if result is not a number
      divide by zero action
   end
else 
   if result is infinite
      divide by zero action
   end
end

0 / 0 is NOT mathematically incalculable -- it is trivially calculable. The problem with 0 / 0 is that any numerical answer is a valid answer. In other words NaN is not a valid result for 0 / 0 but is a description of the character of those answers. (The result can be any of an infinite variety of numbers and not just "a" single number.) This is a problem in mathematics because the result, by itself, is not sufficient to prove anything. Thus, we at times use limits and other constructs to reason about cases involving 0 / 0. A less deceptive result than NaN for 0 / 0 would be "Any Number", but to my knowledge no languages implement that. --Rdm 18:19, 18 June 2010 (UTC)

Maybe it's correct as multiple numbers are Not a Number :-)
(Being pedantic seems to be catching). --Paddy3118 18:37, 18 June 2010 (UTC)

"In other words NaN is not a valid result for 0 / 0 but is a description of the character of those answers." --Rdm 19:17, 18 June 2010 (UTC)

I don't know what "mathematically incalculable" means, but I can testify that in pure mathematics, division by zero, regardless of the dividend, is undefined. Expressions such as $\lim _{x\to 0}{\frac {x^{2}}{x}}$, though they may appear to involve division by zero, actually don't. This expression, for instance, means "the number y such that for all positive ε there exists a positive δ such that for all $x\in (-\delta ,\delta )$, $\left|{\frac {x^{2}}{x}}-y\right|<\epsilon$", i.e., 0. —Underscore (Talk) 01:04, 19 June 2010 (UTC)

According to the wikipedia "In mathematics, defined and undefined are used to explain whether or not expressions have meaningful, sensible, and unambiguous values. Whether an expression has a meaningful value depends on the context of the expression. For example the value of 4 − 5 is undefined if a positive integer result is required." And the problem with 0/0 is the cardinality of the result, not the lack of any results. --Rdm 11:37, 19 June 2010 (UTC)

I don't know of any conventional mathematical context in which "${\frac {1}{0}}$" or "${\frac {0}{0}}$" has a meaningful, sensible, and unambiguous value. —Underscore (Talk) 18:42, 19 June 2010 (UTC)