The only correct answer. In situations like this there is zero point trying to reason with the people who are wrong. People double down in their own echo chamber/bubble. However, if you get another expert in the same field to back you up, it's more likely to get them to relent, or at least chill out.
Or they could triple down and get even more defensive. But that would be embarrassing for them if they are acting that way in front of people outside of the argument. It could go either way. But since they are already being defensive, it's either do this - or just drop the argument, and quietly tell your child they are wrong. Make it a teaching lesson that sometimes people can be wrong.
The only correct answer is to sit down in a locked sound chamber, find the most eccentric of math professor from the local community college, and have them explain left and right side limits as the equation approaches zero for at least five hours.
I know I would…my 3rd grade daughter was told she was “bad in math” because she solved something in a different way than the teacher. The parent/teacher conference the next day turned into a mini lecture series from me (tenured prof) in the different ways to solve the problem.
Just don't remember it incorrectly, or we'll one day be reading a post of how you tripled down on being right about it and I'm going to screenshot the whole thread to lord over you at that point. For fun and science.
Yes, and do so in front of the teacher while explaining that admitting you made a mistake should never be seen as shameful because it encourages such behavior.
This is so important. Shame and "I told you so" make it so much harder to admit you were wrong. I honestly don't know how certain politically affiliated people might reconcile with others because right now everyone's making it really hard to say you might have made a bad decision. If we want things to be better we have to make it easier for people to admit they were wrong.
That’s pretty inaccurate. Dividing by an incredibly small number just gives you an incredibly large number. Newton divided things by an incredibly large number, producing very tiny shapes that could be approximated in an easy way.
The problem with division by zero is that if you allow it, other parts of math start to break. There’s an infamous “fake proof” where if you define 0/0 as 1 (just like any other number divided by itself), you can use basic algebra to show that 1=2.
Serious answer: Unlike other cases in mathematics (e.g. imaginary numbers), you actually cannot define a value for division by zero, even an abstract one.
Or more precisely before an actual mathematician corrects my computer science imprecision, the definition would be so abstract that none of the properties of numbers or algebra would apply to it, and it would be not meaningfully better than just calling it undefined.
1 divided by 0 is a mistake in a first place. I mean there should be no place in any calculation where such situation occurs. It is an invalid step. Teaching it is equal to undefined without further explanation might give a wrong impression that 'undefined' is a correct result and dividing by 0 is possible.
At least this is what i remember from my math department in uni.
It depends on the context. There are times when it’s useful to think about what would happen in that situation. For example: my car is parked. It needs to go to a store 1 km away. At this speed, how long will it take to get there? 1/0. It will never get there.
If you wanted to be mathematically rigorous you would still try and avoid talking about 1/0 and say something like "1/speed goes to infinity in the limit where speed goes to 0"
It's not a question of learning that 'you can't divide one by zero'. It's a question of learning what division means. That is, the question 'what is a divided by b?' is the same as saying 'which numbers, if any, when multiplied by b will produce a?'
So in this case the question is 'find the set of real numbers that when multiplied by 0 produce 1', which is of course the empty set.
I suspect in this case neither the teacher, the principal, nor the parent has a firm grasp on mathematical reasoning, so we're left with frustrating and fruitless appeals to authority.
Parents (and adults in general) get very upset about "new math" and new ways of doing the same problems. This is so frustrating to me.
Understanding HOW numbers and functions relate to one another is far more useful and applicable than memorization or one-way processes. Learning early on "how many tens are in" creates a reference point for when new concepts like multiplication are introduced. It's long been established that connection to prior knowledge and experience creates deeper learning than that which happens without connection or context.
In other words, the "old way" still works, yes, but might have only been accessible to some. Isn't it our calling and our duty to reach as many students as we can in as many ways as we can? Give them all the methods so that when they become adults they can decide which method works best for them -- they all reach the same solution.
My wife is a math teacher. While I partially agree with you, some of the “methods” that student are being required to use to solve certain problems frankly take twice as long and confuse some students even more. There’s usually several ways to solve problems, and students should be able to use whichever method suits them best. The problem arises when everyone has to use the exact same method. Receiving a zero on a problem for solving it correctly just because the student used a different method should not be a thing. I don’t think parents would care very much about “new math” if their children were given the option of using whichever method they want.
For somebody in Grade 3 a real life example is better than describing sets of real numbers.
You can divide 1 whole cake into two pieces, and each piece represents half of that whole. 1 divided by 2 = 1/2. You can still construct a whole cake out of those two equal halves.
You can divide 1 whole cake into all kinds of numbers of equal pieces. 3 pieces, 4 pieces, 1000 pieces, and still reconstruct the cake to a whole afterwards. But if I ask you to divide1 whole cake into 0 equal pieces, how would you do it?
You don't just get rid of the cake. The cake still exists. You have to be able to reconstruct the cake with the total of pieces that you divided it into. How many pieces would there be? It's 0 pieces. If you have 0 pieces of cake, regardless of what size the pieces of cake those are, it's still zero pieces of cake and you can't reconstruct a whole cake from 0 pieces of cake. And if you have any amount of cake available to you to reconstruct the original cake, then you have more pieces than 0.
“Arguing about math” is dumb, math is facts with proofs. Too many replies just chirp what others have told them or what the calculator shows.
Alternatively you can show that if you accept that division by zero is possible then 1=2
The most interesting thing is that it’s not “wrong” to define division by zero. It simply means you reject a rather large amount of defined math and quite likely you’d struggle to get beyond counting before you get contradictions. It would be fun to get the teacher and principal to re-define (provably) some rather strange math.
Just tell them if they think it’s right they should just enter it in any calculator or calculation software of their choice. They won’t fine one that says it’s 0.
Slight nit but that's just a failure mode of the calculator. It doesn't mean the answer is "infinite" if that's what you were implying. It's undefined. It's basically searching for an answer that doesn't exist.
There are plenty of other calculators with such oversights that would happily spend forever to try and give you an answer. Like say one that tried to provide a counter for the Collatz conjecture.
EDIT: Also nit since "subtraction to zero" doesn't tell you how 1/7=0.142857142...
Nah, go to the local news station and publicly shame the educators for not having the decency to own the mistake...or for being uneducated. Either way.
Think of it as sorting apples into piles. Six apples into two piles is easy, three apples each. Whatever apples into no piles. Can't do that. So it's undefined.
Went way too far down to find this answer. It seems like there should be an answer because every other number you plug into the operation works. -12/3 = -4 for example. When you divide you are putting things into groups. The question asked by the operation of 1 divided by 0 is basically "How would you divide an apple into equal pieces of nothing?" Which is a nonsense question, hence why it is undefined. The question and hence the equation are inoperable.
I always have thought of division as "how many A's fit into B's" and extending that to 1/0 is a non-sensical "how many nothings fit into one?" but in that light infinity would make sense as an answer.
dividing is just a fancy way of subtracting. If you say 20 / 5, you're subtracting 5 as many times as you can (4). And thus the inverse, 4 x 5 (or adding 5, 4 times) you get 20.
If you say 1 / 0, how many times can you subtract 0 from 1? An infinite number of times. But an infinite number of zeros can never add up to 1.
So 1 / 0 both is, and isn't infinite. Thus it's undefined.
I watched my math teacher show that dividing by 0 lets you say 1=2, and that's obviously wrong.
I was taught in 3rd grade that it rains so clouds could get light enough to get over the mountains.
I repeated this answer in 6th grade and was asked "where did you learn that?" and named names cause fuck you to trifling-ass 3rd grade teachers and your lying to kids cause you don't know shit. Deserve to be called out making a kid look stupid later in life.
Excuse me: I seem to recall 0/0 is also undefined, Making it x/0 undefined, and never infinite, in all cases. (in real. I think also complex, but am a bit rusty on that)
It is the limit of x/0 that is infinite, but not x/0 itself.
Edit: I seem to be getting a lot of correcting responses from people who did not see the original post that I was reacting to, which claimed 0/0 is infinite. My reaction made a lot more sense in that context.
The limit is negative infinity when approaching zero from negatives and positive infinity when approaching zero from positives. It's a very good way of visualizing why it's undefined in an analytical way because it diverges the closer you get. (But there are special situations that define a point at infinity.)
Algebraically, dividing by 0 is undefined from simple ring properties.
x/0 is undefined (or infinity), for all real x (except zero)
Slight correction: it approaches infinity as the denominator approaches zero and x is positive. If x is negative it approaches negative infinity and if the denominator is 0 then the expression is undefined.
I don’t know if it’s bait or not, but I know personally a few people who had this happen to their kids in school, including me. All different schools and teachers. It seems like a not-uncommon confusion among third grade teachers.
This specific story may be bait, but I don't doubt that shit like this happens all the time. I had so many run-ins with smugly incorrect teachers in elementary school and high school, it was a nightmare. Uni was such a breath of fresh air.
Not always, but here I think it is helpful to see that 1/0=0 would break this pattern (also introducing the idea of limits and approaching a value to approximate it this early might be awesome for the kid‘s math development)
I remember being angry in like 4th grade because I read a bunch and was always a good speller and on a spelling test I missed the word 'lightning'. The teacher said it was spelled 'lightening', and I was like that's a whole different word and the word you described was lightning from a thunderstorm, not the 'lightening' of a dark space. But she didnt listen; i guess she thought they were spelled the same way.
I was young when I realized that teachers are people too and don't know everything. I remember it was the first day of health class and while he was going over all the topics we would be learning about he got to voluntary vs involuntary systems.
He said your lungs are a voluntary system because it volunteers to breath for you.
This is so old. But one could ask the teacher to prove it. The answer is either infinity or minus infinity, depending of how you're approaching it. Hence it's undefined. The proof is fairly simple: you just divide by smaller and smaller numbers and find out that the results become increasingly larger numbers, hence +/- infinity.
That's when you use apples. Take two apples and ask her to show you how you divide by 2. Making 2 groups. How many apples in each group. Divide by 1. Make 1 group of apples. How many apples are in that group. Now divide by zero groups. See how she explains that.
1÷0 doesn't matter for a second grade kid but you also shouldn't be telling that it equals 0 rather infinity works better. Or you can simply say not defined.
Might not be in the curriculum but from a question a kid asked.
When I was in first grade we were told to come up with our own subtractions to practice carrying over, and my teacher had to call another one to figure out mine:
1000 - 299.
Carrying over more than once took them both a while. I don't know if this was the point when I lost respect for authority, but it certainly helped. I still prefer, by far, a person who can say "I don't know, let me ask for help" over the ones who double down on confidently being wrong.
I regularly meet adults who can't handle the idea of discontinuities in math. I can imagine a teacher just telling a kid that it's "zero" so she doesn't have to deal with a child's reaction to "You can't divide by zero".
I had a whole meeting with a project manager once because I was using negative infinity and positive ifinity instead of 0 or an arbitrarily large number as a timer sentinel, and he could not grasp that the downstream consequences of magic values for timer sentinels will eventually cause nightmares that will land back on my desk. Dumbass genuinely believed I was just being "fancy". --Nah motherfucker, we initialize a timestamp that stores the last time something happened as negative infinity, and indefinite lockouts as positive infinity, because it will always pass a check where (t - c > n < c - t). 0 does not have this guarantee, and inducing a null-check in the code is a waste of time when infinity has the same logical result as a logic ejection.
Dividing by 0 makes no sense. A division is asking how many times does that number fit into that number?
10/2 means 2 fits 5 times in 10.
10/0,5 means 0,5 fits 20 times in 10.
10/0 has no meaning. How many times does nothing fit in 10? It could be 0, it could be infinite, it could be "banana", no answer is wrong nor correct thus undefined.
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