A community for students.
Here's the question you clicked on:
 0 viewing
SolomonZelman
 one year ago
just a very quick though about division by 0.
SolomonZelman
 one year ago
just a very quick though about division by 0.

This Question is Closed

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.4It 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 twosided 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
 one year ago
Best ResponseYou've already chosen the best response.0I 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
 one year ago
Best ResponseYou've already chosen the best response.4would you agree that \(\Large\color{black}{ \displaystyle \frac{1}{~~\frac{1}{2}~~}=2 }\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah. \[\frac{1}{\frac{1}{2}}=1*2\]

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.4yes, 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
 one year ago
Best ResponseYou've already chosen the best response.0So 3,4,5 to infinity? Or to a limit?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.4don'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
 one year ago
Best ResponseYou've already chosen the best response.4this way, you are going to get an infinitely large output.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.4now, 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
 one year ago
Best ResponseYou've already chosen the best response.4Also: 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
 one year ago
Best ResponseYou've already chosen the best response.4you 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
 one year ago
Best ResponseYou've already chosen the best response.4sorry for dumping all of this on you.... u will get to this later.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0haha, it's fine. It's pretty complicated but it's real interesting stuff :)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.4Yeah, 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
 one year ago
Best ResponseYou've already chosen the best response.0No 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
 one year ago
Best ResponseYou've already chosen the best response.4There 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
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, I've seen the word representations on those before. They're a simple way of representing something so complex.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.4yes, 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
 one year ago
Best ResponseYou've already chosen the best response.0Well 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
 one year ago
Best ResponseYou've already chosen the best response.4i used \Large in front of the latex

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh ok, thanks a ton for everything :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.