7 ms·

Yesterday on my X timeline there was a woman explaining how her daughter's teacher had told the kids that 1/0=0. The woman wrote to the teacher to explain that

by dudul 3y ago

Yesterday on my X timeline there was a woman explaining how her daughter's teacher had told the kids that 1/0=0. The woman wrote to the teacher to explain that no, this is incorrect. The teacher got so mad she looped in the principal who sided with the teacher. Parents, teach your kids that even teachers make mistake and can be petty :) and also, that you can't divide by zero...

kazinator 3y ago
s/even/particularly/
Salgat 3y ago
https://www.reddit.com/r/NoStupidQuestions/comments/18896hw/my_sons_third_grade_teacher_taught_my_son_that_1/ https://www.reddit.com/r/NoStupidQuestions/comments/18896hw/... You're referring to this reddit post.
- notfed 3y ago
  The Reddit responses to this are an army of bikeshedding nerd-Karens poised for war over something very trivial.
ykonstant 3y ago
Amusingly, in the Lean proof assistant, division by zero in both Naturals and Integers results in zero: #eval (1/0 : Nat) -- 0 #eval (1/0 : Int) -- 0 There are good reasons for this convention in the context of Lean, although I doubt that teacher had formal verification in mind :D
- noodlesUK 3y ago
  I feel like a proof assistant is amongst the worst places to have something like this rather than (I don’t know how lean works) raising an error. What are the justifications for this convention?
  - colanderman 3y ago
    You typically can't "raise an error" in such contexts in formal reasoning tools. There's no "runtime" per se to raise an error from -- the expressions themselves are manipulated to derive truths -- the division by zero may simply be implicit e.g. in a statement about division by some arbitrary number. Trying to solve the problem with e.g. dependent typechecking quickly gets complicated (both implementation and theory). And adding a concept such as infinity may complicate proofs which now need to deal with infinity being a "number" but which behaves differently from other numbers. Thankfully mathematics has the nice property that you can define concepts any way you want so long as they're self-consistent and match one's expectations. So rather than treating division by zero as an exceptional case -- either by disallowing it in the typesystem, "raising an error", or by introducing a "special" value -- some (most?) verification languages simply define division by zero to have a numeric value, and make it known that this is the case. Users know that they must then write expressions to be explicit about division by zero if they care about that case. (This turns out to be not much different than having to write expressions to satisfy a dependent type system.)
    - isilofi 3y ago
      Yes, but to make this "self-consistent" 0 * 0 = 1 would need to hold. And I'm totally sure that they don't have that...
      - librexpr 3y ago
        ((x / y) * y) = x is not a true statement about real numbers, regardless of if division by zero is defined as an error or as being equal to 0. The true statement is ( y != 0 -> ((x / y) * y) = x ), and this holds no matter how you define division by zero. More generally, in normal math, every theorem that involves division by some value Y which could be zero must have as hypothesis that Y is not equal to zero. All these theorems still work in systems like Lean where division by zero is defined to be zero, so nothing is lost.
    - creata 3y ago
      > You typically can't "raise an error" in such contexts in formal reasoning tools. You could write all your formulas in the Maybe / Option monad (which I guess is the same as 'introducing a "special" value') but that sounds painful...
- thaumasiotes 3y ago
  > There are good reasons for this convention in the context of Lean There are good reasons for the convention of assigning nonsense values to computations that are formally invalid. The convention is so important that it is introduced in the Natural Number Game, where the remarks include a brief discussion of why the predecessor of 0 is defined to be 37. I don't think there's any particular reason why you'd assign 0 as the nonsense value?
tikhonj 3y ago
The worst part is that they are both, in a critical sense, wrong. There is no absolute 100% universal "right" answer to how division works—it's just a matter of convention! Merely getting into the argument of whether 1/0 "is" 0 is wrong. There are practical reasons why we leave division by 0 undefined in "normal" arithmetic but we could, just as easily, operate in a world where 1/0 is defined. In some contexts, 1/0 = 0 is a totally sensible convention! In others, we can define it to be ∞ or, hell, something else entirely. This approach of teaching math as a bunch of universal facts that are either true or false is actively harmful—but super convenient for top-down education and assessment!—because it teaches people the wrong way to think about math or even about conceptual models in general.
- 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?
dylan604 3y ago
I taught a friend's elementary aged kid that 1 + 1 = 10, who then got into trouble for arguing with her teacher. Even after saying that 1+1=10 in binary, she got in trouble for being argumentative even if she wasn't wrong. Apparently, making the teacher look bad in front of the class is frowned upon.
- Jap2-0 3y ago
  As someone studying education... you're right, but you're also kind of a prick. Actually, let me rephrase. It's a bad situation all-round. I assume you didn't tell your friend's kid to go in and argue with her teacher. (If you did, then you are a prick. Otherwise, I rescind the above.) At that age, kids want to tell people when they learn fun or exciting things (well, that's not really restricted to that age), but they don't always think through the effects of saying them. Now, I definitely do know a number of elementary teachers who aren't great at math, but even if the teacher is good at math, imagine their perspective. Off the top of my head, I can only think of a small number of options: 1. agree, move on, and have a bunch of kids who are either confused or are going around telling everyone they know "1 + 1 = 10" without understanding why; 2. scrap whatever lesson they were supposed to do and go into a long, unplanned explanation of how different number bases work and interact with place value; 3. tell the girl she's wrong. Quite frankly, none of these are good options. I can't really fault you for teaching her fun math, but for an elementary teacher that's a really rough spot to be put in. And yes, letting everyone be argumentative all the time is how classroom management goes out the window.
  - falalalala 3y ago
    A big issue in the west is the school system will put lot of effort trying to teach children it deems "special need" but will shut down ASAP the ones curious enough to learn something outside the curriculum. Fact is, school is where intellectual curiosity goes to die.
  - dylan604 3y ago
    yes, i'm a prick for exposing curious kids to stuff outside of their class' curriculum. heaven forbid someone providing learning more advanced than the other students. it's people like you that are pricks for thinking that anyone with extra learning are punishing everyone else in class. it's never a problem for keeping students ready to advance faster than the rest of class keeping them all held back at the slower pace. you're also a prick for assuming the way the conversation came about. you're a prick for not thinking that the conversation was about how math can be fun where things that are simple and considered basic can be different and more advanced where 1+1=2 can also be 1+1=10. but now, you just go off and assume i'm a dick saying 1+1=2 is wrong and the correct answer is 1+1=10 or whatever nonsense led you to thinking i'm a prick.
deleted 3y ago
[deleted]

by dudul 3y ago

kazinator 3y ago

s/even/particularly/

Salgat 3y ago

https://www.reddit.com/r/NoStupidQuestions/comments/18896hw/my_sons_third_grade_teacher_taught_my_son_that_1/ https://www.reddit.com/r/NoStupidQuestions/comments/18896hw/... You're referring to this reddit post.

notfed 3y ago
The Reddit responses to this are an army of bikeshedding nerd-Karens poised for war over something very trivial.

ykonstant 3y ago

Amusingly, in the Lean proof assistant, division by zero in both Naturals and Integers results in zero: #eval (1/0 : Nat) -- 0 #eval (1/0 : Int) -- 0 There are good reasons for this convention in the context of Lean, although I doubt that teacher had formal verification in mind :D

noodlesUK 3y ago
I feel like a proof assistant is amongst the worst places to have something like this rather than (I don’t know how lean works) raising an error. What are the justifications for this convention?
- colanderman 3y ago
  You typically can't "raise an error" in such contexts in formal reasoning tools. There's no "runtime" per se to raise an error from -- the expressions themselves are manipulated to derive truths -- the division by zero may simply be implicit e.g. in a statement about division by some arbitrary number. Trying to solve the problem with e.g. dependent typechecking quickly gets complicated (both implementation and theory). And adding a concept such as infinity may complicate proofs which now need to deal with infinity being a "number" but which behaves differently from other numbers. Thankfully mathematics has the nice property that you can define concepts any way you want so long as they're self-consistent and match one's expectations. So rather than treating division by zero as an exceptional case -- either by disallowing it in the typesystem, "raising an error", or by introducing a "special" value -- some (most?) verification languages simply define division by zero to have a numeric value, and make it known that this is the case. Users know that they must then write expressions to be explicit about division by zero if they care about that case. (This turns out to be not much different than having to write expressions to satisfy a dependent type system.)
  - isilofi 3y ago
    Yes, but to make this "self-consistent" 0 * 0 = 1 would need to hold. And I'm totally sure that they don't have that...
    - librexpr 3y ago
      ((x / y) * y) = x is not a true statement about real numbers, regardless of if division by zero is defined as an error or as being equal to 0. The true statement is ( y != 0 -> ((x / y) * y) = x ), and this holds no matter how you define division by zero. More generally, in normal math, every theorem that involves division by some value Y which could be zero must have as hypothesis that Y is not equal to zero. All these theorems still work in systems like Lean where division by zero is defined to be zero, so nothing is lost.
  - creata 3y ago
    > You typically can't "raise an error" in such contexts in formal reasoning tools. You could write all your formulas in the Maybe / Option monad (which I guess is the same as 'introducing a "special" value') but that sounds painful...
thaumasiotes 3y ago
> There are good reasons for this convention in the context of Lean There are good reasons for the convention of assigning nonsense values to computations that are formally invalid. The convention is so important that it is introduced in the Natural Number Game, where the remarks include a brief discussion of why the predecessor of 0 is defined to be 37. I don't think there's any particular reason why you'd assign 0 as the nonsense value?

tikhonj 3y ago

The worst part is that they are both, in a critical sense, wrong. There is no absolute 100% universal "right" answer to how division works—it's just a matter of convention! Merely getting into the argument of whether 1/0 "is" 0 is wrong. There are practical reasons why we leave division by 0 undefined in "normal" arithmetic but we could, just as easily, operate in a world where 1/0 is defined. In some contexts, 1/0 = 0 is a totally sensible convention! In others, we can define it to be ∞ or, hell, something else entirely. This approach of teaching math as a bunch of universal facts that are either true or false is actively harmful—but super convenient for top-down education and assessment!—because it teaches people the wrong way to think about math or even about conceptual models in general.

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?

dylan604 3y ago

I taught a friend's elementary aged kid that 1 + 1 = 10, who then got into trouble for arguing with her teacher. Even after saying that 1+1=10 in binary, she got in trouble for being argumentative even if she wasn't wrong. Apparently, making the teacher look bad in front of the class is frowned upon.

Jap2-0 3y ago
As someone studying education... you're right, but you're also kind of a prick. Actually, let me rephrase. It's a bad situation all-round. I assume you didn't tell your friend's kid to go in and argue with her teacher. (If you did, then you are a prick. Otherwise, I rescind the above.) At that age, kids want to tell people when they learn fun or exciting things (well, that's not really restricted to that age), but they don't always think through the effects of saying them. Now, I definitely do know a number of elementary teachers who aren't great at math, but even if the teacher is good at math, imagine their perspective. Off the top of my head, I can only think of a small number of options: 1. agree, move on, and have a bunch of kids who are either confused or are going around telling everyone they know "1 + 1 = 10" without understanding why; 2. scrap whatever lesson they were supposed to do and go into a long, unplanned explanation of how different number bases work and interact with place value; 3. tell the girl she's wrong. Quite frankly, none of these are good options. I can't really fault you for teaching her fun math, but for an elementary teacher that's a really rough spot to be put in. And yes, letting everyone be argumentative all the time is how classroom management goes out the window.
- falalalala 3y ago
  A big issue in the west is the school system will put lot of effort trying to teach children it deems "special need" but will shut down ASAP the ones curious enough to learn something outside the curriculum. Fact is, school is where intellectual curiosity goes to die.
- dylan604 3y ago
  yes, i'm a prick for exposing curious kids to stuff outside of their class' curriculum. heaven forbid someone providing learning more advanced than the other students. it's people like you that are pricks for thinking that anyone with extra learning are punishing everyone else in class. it's never a problem for keeping students ready to advance faster than the rest of class keeping them all held back at the slower pace. you're also a prick for assuming the way the conversation came about. you're a prick for not thinking that the conversation was about how math can be fun where things that are simple and considered basic can be different and more advanced where 1+1=2 can also be 1+1=10. but now, you just go off and assume i'm a dick saying 1+1=2 is wrong and the correct answer is 1+1=10 or whatever nonsense led you to thinking i'm a prick.

deleted 3y ago

[deleted]