Is it wrong to tell children that $1/0 =$ NaN is incorrect, and should be $∞$?

I got on television and also heard a papa doubting his children concerning mathematics. The youngsters were possibly concerning 11 or 12 years of ages.

After numerous extra ordinary inquiries he asked his little girl what $1/0$ reviewed to. She mentioned that it had no solution. He asked that informed her that and also she claimed her educator. He after that mentioned that her educator had "taught it wrong" and also it was in fact $∞$.

I assumed the Dad is declaration was a little untrustworthy. Does that feel like practical perspective? I intend this inquiry is partially concerning principles.

2022-07-25 20:45:56
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Answers: 3

You ask:

Is it wrong to tell children that 1/0 = NaN is incorrect, and should be $\infty$.

(My) answer:

Absolutely. When we talk about multiplication and division with numbers, I think that it important to get things right. If people would only grow up learning that $\infty$ is not a (real) number, then I think that it would relieve a lot of confusion about how math treats infinity. And it is definitely not right to say that the statement "$1 / 0$ is not defined" is incorrect. That is what is taught in all basic calculus classes. Why would this be incorrect?

Now, if the question is whether one can ever come in a situation where it is appropriate to write $\frac{1}{0} = \infty$, then the answer is definitely yes. This is illustrated in some of the other answers to your questions. But to say that $1$ divided by $0$ is infinity and then just stop, then I would agree that this is wrong (I might even go so far as to call it irresponsible).

When people ask me why we can't divide by $0$ and if they don't want to "leave it", then I would simply start talking about groups and rings and fields as sets with the operations. When you do that carefully you clearly see why it doesn't make sense.

The wonderful thing about math is that we never have to answer why something isn't defined, the burden of proof is in the hands of the person who claims that something is true.

2022-07-25 22:39:46

I'm sorry yet I assume there is a little false impression below: 1/0 is not infinity, never ever was, never ever will certainly be. This would indicate that $$0\cdot\infty = 1$$ which is definitely incorrect.

The proper mathematical formula is $$\lim_{x \to 0+}(1/x) = +\infty$$ The educator is consequently right, and also it is in fact the moms and dad that was incorrect. 1/0 is undefined, therefore is $$0*\infty$$ also in regard to restrictions.

2022-07-25 21:17:24

As @hardmath indicated there is indeed a floating point representation for infinity.


To address the non-math side of this question. IMHO, it was bad form for the father to contradict authority to his child and sets a bad example without setting a better attitude such as "there may be another answer". I think... it's infinity, what do you think? Here he shows his child he can be vulnerable have a different opinion, even if it technically wrong, and that can be OK if you consider the possibility that someone could be wrong and find a way to verify supposition of facts and confirm or deny them in a rational non-confrontational way. That also demonstrates tolerance and rational objectivity to determine truth by asking if she knows the reason in a non-confrontational way and learn to discuss differences of opinions without fear of criticism as overheard in this example.

" If 'a' is zero and the payload is zero, then it represents infinity." Is the technical reason why the teacher was correct.

However for teaching purposes such as the concept of the distance of the universe, the Big Bang and the weight of an atom, it may be useful to consider teaching in "metaphors" so that approaching a zero numerator or denominator, which may become a when you approach infinity with a real number.

It is also useful to define the order of rules when the paradox of;

  1. "anything multiplied by zero is zero" which contradicts...
  2. "anything divided by zero is infinity"

    • ...Actually (2) really bad boo boo ;) (2.) is not true, as it is only a conditionally true if the numerator is also zero, otherwise, it is NaN.

So explain to the child that 0/0 is a special case with religion. ;) or something of

Fun Fact: Thanks to who introduced the infinity symbol to mathematical literature with his works on the collisions of heavenly bodies at university in the women's dorm. Consider how fortunate we are that we dont have to call it a Wallis instead of ∞ infinity. However John eventually got his immortality with an asteroid in 2000 and

2022-07-25 21:16:43