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November 15th, 2015, 10:38 PM  #21 
Global Moderator Joined: Dec 2006 Posts: 20,633 Thanks: 2080 
It's evidently infinite. If it were finite, that would mean there were only, say, n positive integers, which would make n+1 a bit hard to explain!

November 16th, 2015, 12:54 AM  #22 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
Most mathematicians prefer indeterminate to undefined. The reason we say that $\dfrac{0}{0}$ is indeterminate is because it can be "equal" to any real number. You'll need some understanding of limits if you want a thorough explanation. There are plenty of indeterminate values in maths: $\dfrac{x}{0}$ (for any x), $\infty  \infty$ and $\dfrac{\infty}{\infty}$ are some of them. Strangely, $1^\infty$ is also an indeterminate form. 
November 16th, 2015, 02:07 PM  #23 
Member Joined: Nov 2015 From: New York State Posts: 41 Thanks: 0 
OK, x/0 = indeterminate 1^infinity = indeterminate infinity  infinity = indeterminate infinity / infinity = indeterminate So x/0 = 1^infinity = infinity  infinity = infinity / infinity 
November 16th, 2015, 09:14 PM  #24 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
No. "Indeterminate" is not a number, so all those equals signs you used are wrong.

November 17th, 2015, 02:52 AM  #25 
Member Joined: Nov 2015 From: New York State Posts: 41 Thanks: 0 
x/x=1 0/0=1 0/0=0 Given x/x=1 you can not have both 0/0=1 and 0/0=0. 
November 17th, 2015, 03:46 AM  #26 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,657 Thanks: 2635 Math Focus: Mainly analysis and algebra 
$x/0$ is only indeterminate for $x=0$. For all other values of $x$ it is undefined.

November 17th, 2015, 03:49 AM  #27 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,657 Thanks: 2635 Math Focus: Mainly analysis and algebra 
You should note that language is neither fixed nor precise  unlike mathematics which both (barring new discoveries). There is thus no 1to1 mapping between the two.


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