On: Why you can't divide by zero

[noam_k]

> 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 → noam_k]

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 → tikhonj]

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.

[zmgsabst → tikhonj]

> 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.

[kazinator → tikhonj]

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 → kazinator]

    ceil(0.000001) = 1
    ceil(0) =... 0? Wtf?

But that's a perfectly well defined function. Not every function has to be continuous.

[kazinator → scatters]

In the first place, not every function has to be defined everywhere.

[jjgreen → kazinator]

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. :-)

[imetatroll → tikhonj]

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[dang → imetatroll]

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.

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.

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