SolomonZelman
  • SolomonZelman
just a very quick though about division by 0.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
SolomonZelman
  • SolomonZelman
It is correct to define the division by zero, as \(\Large\color{black}{ \displaystyle \lim_{{\rm n}\rightarrow~0}~\left(\frac{1}{\rm n}\right) }\) --------------------------------------------- because \(\Large\color{black}{ \displaystyle \lim_{{\rm n}\rightarrow~0}~\left(\rm n\right) }\) is zero, and dividing by zero gives (with the application of the limit properties)... \(\Large\color{black}{ \displaystyle \frac{1}{0}=\frac{1}{\displaystyle\lim_{{\rm n}\rightarrow~0}\left(\rm n\right)}=\displaystyle \lim_{{\rm n}\rightarrow~0}~\left(\frac{1}{\rm n}\right) }\) we could be dividing any number doesn't have to be a 1, it is just more convenient to see the point this way. ---------------------------------------------- Now, we know that \(\Large\color{black}{ \displaystyle \lim_{{\rm n}\rightarrow~0^+}~\left(\frac{1}{\rm n}\right) }\) diverges to \(+\infty\) and \(\Large\color{black}{ \displaystyle \lim_{{\rm n}\rightarrow~0^-}~\left(\frac{1}{\rm n}\right) }\) diverges to \(-\infty\) NOW, division by zero gets even worse, because dividing by zero is a two-sided limit. that, is: \(\Large\color{black}{ \displaystyle \lim_{{\rm n}\rightarrow~0}~\left(\frac{1}{\rm n}\right) }\) and this way, the limit diverges to \(+\infty\) and \(-\infty\) all at once. Clearly, this makes no sense. How can one point diverge to both infinities? (there is only 1 point, it can't tear apart and go both directions) the (obvious) CONCLUSION is: division by zero makes no sense.
anonymous
  • anonymous
I wish I could say I understood this. But this reminds of me of that large "proofs of why you can't divide by 0" thread that was up a while ago.
SolomonZelman
  • SolomonZelman
would you agree that \(\Large\color{black}{ \displaystyle \frac{1}{~~\frac{1}{2}~~}=2 }\)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
Yeah. \[\frac{1}{\frac{1}{2}}=1*2\]
SolomonZelman
  • SolomonZelman
yes, and tell me what do you get if: \(\Large\color{black}{ \displaystyle \frac{1}{~~\frac{1}{3}~~}=? }\) \(\Large\color{black}{ \displaystyle \frac{1}{~~\frac{1}{4}~~}=? }\) \(\Large\color{black}{ \displaystyle \frac{1}{~~\frac{1}{5}~~}=? }\) and on....
anonymous
  • anonymous
So 3,4,5 to infinity? Or to a limit?
SolomonZelman
  • SolomonZelman
don't use the word limit. yes, because the smaller number you divide by, (and this number will approach to zero as much as you would like) the bigger output you get
SolomonZelman
  • SolomonZelman
this way, you are going to get an infinitely large output.
SolomonZelman
  • SolomonZelman
now, we can do same thing from negative numbers \(\Large\color{black}{ \displaystyle \frac{1}{~~-\frac{1}{2}~~}=-2 }\) \(\Large\color{black}{ \displaystyle \frac{1}{~~-\frac{1}{3}~~}=-3 }\) \(\Large\color{black}{ \displaystyle \frac{1}{~~-\frac{1}{4}~~}=-4 }\) and so on.... so as you take \(\Large\color{black}{ \displaystyle \frac{1}{~~-\frac{1}{very~~large~~number}~~} }\) you are then going to get an output which will tend to negative infinity closer and closer the bigger "very bg number" you choose
SolomonZelman
  • SolomonZelman
Also: a "limit", just literally means a "limit" in an English sense of it. In other words, and expression is limited to a certain number/value. this value is called "limit" (such that you can get 5, 0.2, or any C units away from the limit)
SolomonZelman
  • SolomonZelman
you can't get a certain number of units close to positive or negative infinity. that is why when your limit is infinity, the limit doesn't exist. (technically speaking "it diverges")
SolomonZelman
  • SolomonZelman
sorry for dumping all of this on you.... u will get to this later.
anonymous
  • anonymous
haha, it's fine. It's pretty complicated but it's real interesting stuff :)
SolomonZelman
  • SolomonZelman
Yeah, it is even more interesting when it comes to gamma functions cycle integrals and all that... but, anyway, ... it was a nice recap:) tnx for participation
anonymous
  • anonymous
No problem, it would've been fun to see this in the other thread. That one had a lot of other good explanations about dividing by 0.
SolomonZelman
  • SolomonZelman
There is also a pizza thing. You can't divide evenly your 6 slice- pizza, to 0 of your friends, because how any will each get. (that is not a complete disprove, as that denies dividing by rational numb. as well)
anonymous
  • anonymous
Yeah, I've seen the word representations on those before. They're a simple way of representing something so complex.
SolomonZelman
  • SolomonZelman
yes, my favorite one. On wiki, when I read some math I get lost at times even though the math it is about is a topic i know.
anonymous
  • anonymous
Well anyways, thanks a bunch for the explanation. It'll probably take a little while for my head to completely wrap around the concepts though. As a final question, how did you get your latex writing to be so big? Still kinda new to writing in latex.
SolomonZelman
  • SolomonZelman
i used \Large in front of the latex
anonymous
  • anonymous
Oh ok, thanks a ton for everything :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.