4 ms·

You know.. dividing is like breaking something up.. If you divide by 2, you break it up into 2 pieces.. if you divide by 0, from some standpoints, you do have n

You know.. dividing is like breaking something up.. If you divide by 2, you break it up into 2 pieces.. if you divide by 0, from some standpoints, you do have nothing, because you broke it up into 0 pieces, and 0 pieces is 0.

hk__2 8y ago
> You know.. dividing is like breaking something up.. If you divide by 2, you break it up into 2 pieces.. if you divide by 0, from some standpoints, you do have nothing, because you broke it up into 0 pieces, and 0 pieces is 0. And dividing by 0.5 is breaking into how many pieces exactly?
- ricardobeat 8y ago
  The analogy actually holds - below 1 it reverses and you 'unbreak' your something (which is now halved) into a larger one.
- jonshariat 8y ago
  I guess its more flipped. How many pieces equal the whole, not how many pieces can the whole be broken up into. That's why you can't divide by 0, any number of nothing can't make a whole. *disclamer: I have no math background whatso ever
  - ggggtez 8y ago
    The function "division" is just like any other function. It takes two inputs, and gives an output. The reason it's a useful function is it has some properties: y=1/x is continuous except where x==0. That is, as you approach 0 from either side, it grows to either +- infinity. The developers of this language want to make this function ==0 when x is 0. You can do that, sure, but it doesn't change the fact that when you go from +0.0000001 to -0.0000001, you now have 2 non-continuous jumps instead of just one.
    - jonshariat 8y ago
      ah thanks for the explanation!
- jonshariat 8y ago
  I guess its more flipped. How many pieces equal the whole, not how many pieces can the whole be broken up into. That's why you can't divide by 0, any number of nothing can't make a whole. So all that to say: We can't treat 0 like a number. *disclaimer: I have no math background whatsoever, this is just a fun topic.
  - halflings 8y ago
    And as it follows, if you divide by 0.00000000001, you can fit a whole lot of pieces in your original value... so what should dividing by 0 (which is even smaller than 0.000000001) naturally do? 0, or +infinity?
- inglor 8y ago
  I love how people without an actual mathematical background make these sort of arguments - not because they're wrong but because it helps me check when I make those assumptions myself. Multiplying by the square root of 2 is also a fun one since you need limits to show people that real numbers only make sense with the least upper bound theorem and limits and things they expect to work "intuitively" (like division or multiplication) only have approximate meaning when they use the common operations.
- upofadown 8y ago
  We are talking about machine integers here... So division is actually all about evenly dividing counts of things with the possibility that you might have some left over. Reals are fundamentally different and are not found in things like computers and in general are of no practical use. For work with values (as opposed to counts) we use something called floating point.
JadeNB 8y ago
> if you divide by 0, from some standpoints, you do have nothing, because you broke it up into 0 pieces, and 0 pieces is 0. This explains exactly why we shouldn't divide by 0. The pieces after breakage should, if one is so inclined, be able to be re-assembled into the whole; but, once you break something into 0 pieces, it is gone. Thus at best `0/0` could be defined … but the problem there is not that there's no answer but that every answer is equally good.
Confusion 8y ago
You know.. dividing is like breaking something up [..] No. What it is 'like' is totally irrelevant and actively harmful to consider if you want to be able to get anything serious done with your programming language. This is not a place to start philosophizing. For consistent arithmetic it is important to know which axioms are fulfilled. Division needs to be a mathematically clearly defined operation.
derefr 8y ago
I mean, you’re not wrong. Not right either (for technical reasons), but that kind of argument leads you to mathematical objects like the Cantor set: a set of line segments with zero total length. Mathematically, you have a bunch of objects; practically, you have nothing.

hk__2 8y ago

> You know.. dividing is like breaking something up.. If you divide by 2, you break it up into 2 pieces.. if you divide by 0, from some standpoints, you do have nothing, because you broke it up into 0 pieces, and 0 pieces is 0. And dividing by 0.5 is breaking into how many pieces exactly?

ricardobeat 8y ago
The analogy actually holds - below 1 it reverses and you 'unbreak' your something (which is now halved) into a larger one.
jonshariat 8y ago
I guess its more flipped. How many pieces equal the whole, not how many pieces can the whole be broken up into. That's why you can't divide by 0, any number of nothing can't make a whole. *disclamer: I have no math background whatso ever
- ggggtez 8y ago
  The function "division" is just like any other function. It takes two inputs, and gives an output. The reason it's a useful function is it has some properties: y=1/x is continuous except where x==0. That is, as you approach 0 from either side, it grows to either +- infinity. The developers of this language want to make this function ==0 when x is 0. You can do that, sure, but it doesn't change the fact that when you go from +0.0000001 to -0.0000001, you now have 2 non-continuous jumps instead of just one.
  - jonshariat 8y ago
    ah thanks for the explanation!
jonshariat 8y ago
I guess its more flipped. How many pieces equal the whole, not how many pieces can the whole be broken up into. That's why you can't divide by 0, any number of nothing can't make a whole. So all that to say: We can't treat 0 like a number. *disclaimer: I have no math background whatsoever, this is just a fun topic.
- halflings 8y ago
  And as it follows, if you divide by 0.00000000001, you can fit a whole lot of pieces in your original value... so what should dividing by 0 (which is even smaller than 0.000000001) naturally do? 0, or +infinity?
inglor 8y ago
I love how people without an actual mathematical background make these sort of arguments - not because they're wrong but because it helps me check when I make those assumptions myself. Multiplying by the square root of 2 is also a fun one since you need limits to show people that real numbers only make sense with the least upper bound theorem and limits and things they expect to work "intuitively" (like division or multiplication) only have approximate meaning when they use the common operations.
upofadown 8y ago
We are talking about machine integers here... So division is actually all about evenly dividing counts of things with the possibility that you might have some left over. Reals are fundamentally different and are not found in things like computers and in general are of no practical use. For work with values (as opposed to counts) we use something called floating point.

JadeNB 8y ago

> if you divide by 0, from some standpoints, you do have nothing, because you broke it up into 0 pieces, and 0 pieces is 0. This explains exactly why we shouldn't divide by 0. The pieces after breakage should, if one is so inclined, be able to be re-assembled into the whole; but, once you break something into 0 pieces, it is gone. Thus at best `0/0` could be defined … but the problem there is not that there's no answer but that every answer is equally good.

Confusion 8y ago

You know.. dividing is like breaking something up [..] No. What it is 'like' is totally irrelevant and actively harmful to consider if you want to be able to get anything serious done with your programming language. This is not a place to start philosophizing. For consistent arithmetic it is important to know which axioms are fulfilled. Division needs to be a mathematically clearly defined operation.

derefr 8y ago

I mean, you’re not wrong. Not right either (for technical reasons), but that kind of argument leads you to mathematical objects like the Cantor set: a set of line segments with zero total length. Mathematically, you have a bunch of objects; practically, you have nothing.