21 ms·

but with floating point units, 1.0/0.0 is infinity.

behringer 8y ago
That's not correct mathematically though. You can't divide something 0 times and get any number. Adding zero + zero + zero infinite times does not equal 1.
- jibal 8y ago
  "That's not correct mathematically though." Yes, certainly it is. "You can't divide something 0 times and get any number. Adding zero + zero + zero infinite times does not equal 1." The discussion is about mathematics, not elementary school arithmetic.
  - behringer 8y ago
    Feel free to give me a proof that adds zeros and gets a number greater than 0.
- Zarel 8y ago
  It's plenty correct mathematically; the linked article even explains this. Generally, your viewpoint comes from an incorrect understanding of mathematics, so let's explore what math actually is: When we say "10 / 2 = 5", the result "5" doesn't come out of nowhere. It comes out of the definition of division. There are several ways you could define division. You could interpret "10 / 2 = 5" as meaning any of: • "If you had a 10-inch stick and you divided it into 2 equal parts, each part would be 5 inches." • "If you had the equation 2 * X = 10, X = 5 would be a solution to it." • "If you had 10 Pa of pressure in an enclosed box, and you increased the volume of the box to 2 times its previous volume, its new pressure would be 5 Pa." • "A wave of wavelength 2cm would have a frequency of 5 per 10cm." These definitions all lead to the same result – in other words, they're equivalent. When this happens, mathematicians usually don't particularly care which one is the "real" definition. This applies to many different mathematical axioms. For instance compare the definition of the Parallel Postulate on Wikipedia: "If a line segment intersects two lines, the two lines will intersect on the side that their angles with the line segment sum up to less than 180°" – https://en.wikipedia.org/wiki/Parallel_postulate https://en.wikipedia.org/wiki/Parallel_postulate with the definition on Wolfram MathWorld: "If you have a straight line and a point not on it, there exists only one straight line which passes through that point and never intersects the first line." – http://mathworld.wolfram.com/ParallelPostulate.html http://mathworld.wolfram.com/ParallelPostulate.html These are different definitions. But since they lead to the same result, mathematicians don't really care to argue over which is the "real" definition. Some definitions only apply over a subset of numbers. For instance, originally, "5 - 10" was undefined. Then negative numbers were invented, to expand the definition. The same thing happened with square roots and complex numbers. That's the same thing with division. 1 / 0 was originally undefined. But you can come up with new number systems that define it, while preserving all the other properties that make division what it is. A common definition is 1 / 0 = Infinity, which is done in the Riemann sphere number system: https://en.wikipedia.org/wiki/Riemann_sphere https://en.wikipedia.org/wiki/Riemann_sphere There's nothing mathematically incorrect about doing any of this.
- dahart 8y ago
  > That’s not correct mathematically though. Floating point infinity is not equal to math infinity. Floating point infinity means there was overflow of the representation we are using, not that the number is larger than any known number. > Adding zero + zero + zero infinite times does not equal 1. Sometimes it does. That’s what an integral is.
  - ordu 8y ago
    Nope. Integral is the sum of infinitesimal values, not zeroes. If you dig into definition of Riemann integral, then you'll see that the are no zeroes in the sum at any step. Except for zeroes of function being integrated, of course. For example Riemann integral is just limit of sums built on tagged partitions of a closed interval with largest sub-interval approaches zero. But no single sub-interval is equal to zero, their lengths just approach zero while being strictly positive values. Calculus does not divide by zero, calculus explores what happens when we move to zero as close as we can and even closer.

That's not correct mathematically though. You can't divide something 0 times and get any number. Adding zero + zero + zero infinite times does not equal 1.

jibal 8y ago
"That's not correct mathematically though." Yes, certainly it is. "You can't divide something 0 times and get any number. Adding zero + zero + zero infinite times does not equal 1." The discussion is about mathematics, not elementary school arithmetic.
- behringer 8y ago
  Feel free to give me a proof that adds zeros and gets a number greater than 0.
Zarel 8y ago
It's plenty correct mathematically; the linked article even explains this. Generally, your viewpoint comes from an incorrect understanding of mathematics, so let's explore what math actually is: When we say "10 / 2 = 5", the result "5" doesn't come out of nowhere. It comes out of the definition of division. There are several ways you could define division. You could interpret "10 / 2 = 5" as meaning any of: • "If you had a 10-inch stick and you divided it into 2 equal parts, each part would be 5 inches." • "If you had the equation 2 * X = 10, X = 5 would be a solution to it." • "If you had 10 Pa of pressure in an enclosed box, and you increased the volume of the box to 2 times its previous volume, its new pressure would be 5 Pa." • "A wave of wavelength 2cm would have a frequency of 5 per 10cm." These definitions all lead to the same result – in other words, they're equivalent. When this happens, mathematicians usually don't particularly care which one is the "real" definition. This applies to many different mathematical axioms. For instance compare the definition of the Parallel Postulate on Wikipedia: "If a line segment intersects two lines, the two lines will intersect on the side that their angles with the line segment sum up to less than 180°" – https://en.wikipedia.org/wiki/Parallel_postulate https://en.wikipedia.org/wiki/Parallel_postulate with the definition on Wolfram MathWorld: "If you have a straight line and a point not on it, there exists only one straight line which passes through that point and never intersects the first line." – http://mathworld.wolfram.com/ParallelPostulate.html http://mathworld.wolfram.com/ParallelPostulate.html These are different definitions. But since they lead to the same result, mathematicians don't really care to argue over which is the "real" definition. Some definitions only apply over a subset of numbers. For instance, originally, "5 - 10" was undefined. Then negative numbers were invented, to expand the definition. The same thing happened with square roots and complex numbers. That's the same thing with division. 1 / 0 was originally undefined. But you can come up with new number systems that define it, while preserving all the other properties that make division what it is. A common definition is 1 / 0 = Infinity, which is done in the Riemann sphere number system: https://en.wikipedia.org/wiki/Riemann_sphere https://en.wikipedia.org/wiki/Riemann_sphere There's nothing mathematically incorrect about doing any of this.
dahart 8y ago
> That’s not correct mathematically though. Floating point infinity is not equal to math infinity. Floating point infinity means there was overflow of the representation we are using, not that the number is larger than any known number. > Adding zero + zero + zero infinite times does not equal 1. Sometimes it does. That’s what an integral is.
- ordu 8y ago
  Nope. Integral is the sum of infinitesimal values, not zeroes. If you dig into definition of Riemann integral, then you'll see that the are no zeroes in the sum at any step. Except for zeroes of function being integrated, of course. For example Riemann integral is just limit of sums built on tagged partitions of a closed interval with largest sub-interval approaches zero. But no single sub-interval is equal to zero, their lengths just approach zero while being strictly positive values. Calculus does not divide by zero, calculus explores what happens when we move to zero as close as we can and even closer.