# Can x/0 be divided out

by ShawnD
Tags: divided, x or 0
 Sci Advisor P: 986 Say I had an expression that went like this $$\frac{ 5 \frac{x}{0} }{3 \frac{x}{0} }$$ Can I divide those $\frac{x}{0}$ terms or do they make the expression undefined?
 Emeritus Sci Advisor PF Gold P: 10,427 Nope, you can't divide them out. The entire expression is indeterminate (NOT undefined). - Warren
 Sci Advisor HW Helper P: 9,396 I wouldn't say you can't divide them out so much as what you wrote is just plain wrong, being polite about it - the symbols make no sense as written.
 Emeritus Sci Advisor PF Gold P: 10,427 Can x/0 be divided out I think he means $$\frac{ 5 \cdot \frac{x}{0} }{3 \cdot \frac{x}{0} }$$ to be read "5 times x over 0...", not "5 and x zeroths..." - Warren
 Sci Advisor HW Helper P: 9,396 But is still makes no sense. x/0 is not a well-defined symbol in the real number system that one can manipulate like this.
 P: 1,004 I think that was part of his question.
 P: 1,210 1/0.1 is tha same as 1*10 1/0.01 is tha same as 1*100 1/0.001 is tha same as 1*1000 and so on ... 1/0 is the same as 1*oo and in both cases we are no longer in a finite system. oo is a general notation for infinity therefore 1/0 is also a general notation for infinity. Please look at: http://mathworld.wolfram.com/Infinity.html
HW Helper
P: 1,123
 Quote by Organic 1/0.1 is tha same as 1*10 1/0.01 is tha same as 1*100 1/0.001 is tha same as 1*1000 and so on ... 1/0 is the same as 1*oo and in both cases we are no longer in a finite system. oo is a general notation for infinity therefore 1/0 is also a general notation for infinity. Please look at: http://mathworld.wolfram.com/Infinity.html
Note for others, in the link given it goes points out:

"Informally,[itex]1 / \infty = 0[/tex] , a statement which can be made rigorous using the limit concept"

You can't just say:

$$\frac{1}{\infty} = 0$$

or any manipulation of that as and think it is mathematically true.