Can You Divide By Zero in Math?

  • Thread starter ShawnD
  • Start date
In summary, the conversation was about whether or not it is possible to divide out the \frac{x}{0} terms in the expression \frac{ 5 \frac{x}{0} }{3 \frac{x}{0} }. It was mentioned that the symbols in the expression do not make sense as written and that x/0 is not a well-defined symbol in the real number system. The concept of infinity was also brought up and it was pointed out that \frac{1}{\infty} cannot be manipulated in the same way as finite numbers. The conversation ended with a suggestion to refer to a link discussing the rigorous use of limits.
  • #1
ShawnD
Science Advisor
718
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Say I had an expression that went like this

[tex]\frac{ 5 \frac{x}{0} }{3 \frac{x}{0} }[/tex]

Can I divide those [itex]\frac{x}{0}[/itex] terms or do they make the expression undefined?
 
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  • #2
Nope, you can't divide them out. The entire expression is indeterminate (NOT undefined).

- Warren
 
  • #3
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.
 
  • #4
I think he means

[tex]\frac{ 5 \cdot \frac{x}{0} }{3 \cdot \frac{x}{0} }[/tex]

to be read "5 times x over 0...", not "5 and x zeroths..."

- Warren
 
  • #5
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.
 
  • #6
I think that was part of his question.
 
  • #7
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
 
  • #8
Organic said:
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:

[tex]\frac{1}{\infty} = 0[/tex]

or any manipulation of that as and think it is mathematically true.
 
  • #9
Discussion over the foundations of limits split to new thread. Please stop hijacking threads.
 

1. Can 0 be divided out of any number?

No, division by 0 is undefined in mathematics. Any number divided by 0 will result in an error or undefined value.

2. What happens when x is divided by 0?

When x is divided by 0, the result is undefined. This is because division by 0 is not possible in mathematics.

3. Is it possible to simplify a fraction by dividing out a 0 in the numerator or denominator?

No, dividing out a 0 in the numerator or denominator does not simplify a fraction. It is still an undefined value.

4. Why is division by 0 not allowed in mathematics?

Division by 0 is not allowed in mathematics because it leads to contradictions and violates the basic principles of arithmetic. It also makes it impossible to define a unique inverse for multiplication.

5. Can dividing by 0 ever be useful?

No, dividing by 0 is not useful in mathematics. It does not provide any meaningful or useful information and can lead to errors in calculations.

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