April 1st, 2019, 11:20 PM  #1 
Member Joined: Oct 2014 From: Mars Posts: 33 Thanks: 0  Why isn't dividing by zero = zero?
In layman terms, why is x divided by 0 equal to undefined, and not 0? If anything slightly above 0 is +infinity, and anything slightly below 0 is infinity, can't we argue that the number in between both infinities is 0? 
April 1st, 2019, 11:26 PM  #2 
Senior Member Joined: Oct 2009 Posts: 772 Thanks: 279  How many times do I need to give you 0 apples in order for you to have 1 apple.

April 1st, 2019, 11:58 PM  #3  
Member Joined: Oct 2014 From: Mars Posts: 33 Thanks: 0  Quote:
Last edited by Apple30; April 2nd, 2019 at 12:05 AM.  
April 2nd, 2019, 01:07 AM  #4 
Senior Member Joined: Oct 2009 Posts: 772 Thanks: 279  
April 2nd, 2019, 01:26 AM  #5  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,150 Thanks: 730 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
More specifically, if you consider a function $\displaystyle f(x) = \frac{g(x)}{x}$ and then try and find the limit of that function as x tends to zero, then the limit obtained is not always zero. It changes depending on what g(x) is. A typical example is $\displaystyle g(x) = \sin x$. If you look at the attached table, which shows somes evaluations of the function with decreasing values of x, the function tends towards 1, not 0.  
April 2nd, 2019, 01:35 AM  #6  
Member Joined: Oct 2014 From: Mars Posts: 33 Thanks: 0  Quote:
 
April 2nd, 2019, 01:56 AM  #7 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,150 Thanks: 730 Math Focus: Physics, mathematical modelling, numerical and computational solutions  
April 2nd, 2019, 05:06 AM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,344 Thanks: 1024 
4 apples divided by 2: Jim and Joe get 2 each 4 apples divided by 1: Jim gets 4 4 apples divided by nobody: ? 
April 2nd, 2019, 07:55 AM  #9  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,640 Thanks: 2624 Math Focus: Mainly analysis and algebra  Quote:
\begin{array}{c  c} x & \frac{\sin x}{x} \\ \hline 0.1\phantom{000} & 0.998334166468282 \\ 0.01\phantom{00} & 0.999983333416667 \\ 0.001\phantom{0} & 0.999999833333342 \\ 0.0001 & 0.999999998333333 \end{array}  
April 2nd, 2019, 12:45 PM  #10 
Senior Member Joined: Jun 2015 From: England Posts: 905 Thanks: 271 
Hey guys, has anyone noticed the date of the first and last posts by the martian OP?


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