4 ms·

> 1/0 = 0 is a totally sensible convention Except that for all other numbers we have 1/x * x = 1, while 0*0 = 0. Defining division by zero this way breaks exis

by noam_k 3y ago

> 1/0 = 0 is a totally sensible convention Except that for all other numbers we have 1/x * x = 1, while 0*0 = 0. Defining division by zero this way breaks existing rules.

tikhonj 3y ago
0 is always going to be a special case for division in real numbers. But how we handle that special case is a matter of convention.
- sarchertech 3y ago
  Of course it’s a matter of convention. But it’s a convention without which the rest of mathematics taught to school children throughout the world falls apart. Calling the color of the sky blue is just a matter of convention as well, but if one random teacher starts calling it green, she’s doing a terrible disservice to her students. It doesn’t matter that there exists some languages without a difference between blue and green.
- kazinator 3y ago
  The "convention" is inconsistent with division by small quantities that get closer and closer to zero. 1/1000000 = 0.000001 ... 1/10 = 0.1 1/1 = 1 1/0.1 = 10 1/0.0001 = 1000 1/0.0000001 = 1000000 ... 1/0 = ... 0? WTF What is the application for 1/0 = 0? Where is this used? Does it actually make a meaningful appearance outside of drunken barroom conversations, and classrooms staffed by clowns?
  - scatters 3y ago
    ceil(0.000001) = 1 ceil(0) =... 0? Wtf? But that's a perfectly well defined function. Not every function has to be continuous.
    - kazinator 3y ago
      In the first place, not every function has to be defined everywhere.
  - jjgreen 3y ago
    Well, if 1/x -> infinity as x -> 0, x > 0, and 1/x -> -infinity as x -> 0, x < 0, then the average of +infinity and -infinity is zero. :-)
- zmgsabst 3y ago
  > 0 is always going to be a special case for division in real numbers. Right — because it’s impossible to have an inverse of zero multiplication. Eg, 0 = 0 + 0 -> 1 = 1 + 1 -> 0 = 1 if you have a multiplicative inverse to 0, and hence you have collapsed your entire system to a single value. These are students we’re still teaching that basic algebraic structure to — that it’s not possible to have a multiplicative inverse to zero. Calling that a “convention” is wrong.
- imetatroll 3y ago
  . . . . . . . . . ------------------------------------------------------->
  - dang 3y ago
    Hey, can you please make your substantive points without shallow dismissals or name-calling? This is in the site guidelines: https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html. If you know more than others, that's great, but in that case the thing to do is to share some of what you know, so others can learn. If you don't want to do that, that's fine, but in that case please don't post. Putdowns and swipes only degrade the discussion. https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sort=byDate&type=comment&query=share%20know%20learn%20by:dang https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor...

by noam_k 3y ago

> 1/0 = 0 is a totally sensible convention Except that for all other numbers we have 1/x * x = 1, while 0*0 = 0. Defining division by zero this way breaks existing rules.

tikhonj 3y ago

0 is always going to be a special case for division in real numbers. But how we handle that special case is a matter of convention.

sarchertech 3y ago
Of course it’s a matter of convention. But it’s a convention without which the rest of mathematics taught to school children throughout the world falls apart. Calling the color of the sky blue is just a matter of convention as well, but if one random teacher starts calling it green, she’s doing a terrible disservice to her students. It doesn’t matter that there exists some languages without a difference between blue and green.
kazinator 3y ago
The "convention" is inconsistent with division by small quantities that get closer and closer to zero. 1/1000000 = 0.000001 ... 1/10 = 0.1 1/1 = 1 1/0.1 = 10 1/0.0001 = 1000 1/0.0000001 = 1000000 ... 1/0 = ... 0? WTF What is the application for 1/0 = 0? Where is this used? Does it actually make a meaningful appearance outside of drunken barroom conversations, and classrooms staffed by clowns?
- scatters 3y ago
  ceil(0.000001) = 1 ceil(0) =... 0? Wtf? But that's a perfectly well defined function. Not every function has to be continuous.
  - kazinator 3y ago
    In the first place, not every function has to be defined everywhere.
- jjgreen 3y ago
  Well, if 1/x -> infinity as x -> 0, x > 0, and 1/x -> -infinity as x -> 0, x < 0, then the average of +infinity and -infinity is zero. :-)
zmgsabst 3y ago
> 0 is always going to be a special case for division in real numbers. Right — because it’s impossible to have an inverse of zero multiplication. Eg, 0 = 0 + 0 -> 1 = 1 + 1 -> 0 = 1 if you have a multiplicative inverse to 0, and hence you have collapsed your entire system to a single value. These are students we’re still teaching that basic algebraic structure to — that it’s not possible to have a multiplicative inverse to zero. Calling that a “convention” is wrong.
imetatroll 3y ago
. . . . . . . . . ------------------------------------------------------->
- dang 3y ago
  Hey, can you please make your substantive points without shallow dismissals or name-calling? This is in the site guidelines: https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html. If you know more than others, that's great, but in that case the thing to do is to share some of what you know, so others can learn. If you don't want to do that, that's fine, but in that case please don't post. Putdowns and swipes only degrade the discussion. https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sort=byDate&type=comment&query=share%20know%20learn%20by:dang https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor...