# Zero/Zero, infinity/infinity = ?

Discussion in 'Physics & Math' started by Saint, Apr 17, 2013.

1. ### SaintValued Senior Member

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Zero/Zero, infinity/infinity = ?

Are they defined?

3. ### eramSciengineerValued Senior Member

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1,877
They aren't. They're undefined.

5. ### TachBannedBanned

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You still haven't learned your prior lesson, have you? Is $\frac{sinx}{x}$ when $x->0$ undefined?

7. ### TachBannedBanned

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The precise answer is given by a well-known calculus theorem.

8. ### mathmanValued Senior Member

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As is, they are undefined. If it is a result of a limiting process (like sinx/x as x -> 0), then there are procedures (L'Hopital's rule) to handle it.

9. ### AlphaNumericFully ionizedRegistered Senior Member

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Infinity is not a member of the Reals and therefore it is meaningless to try to do algebra with it unless you define the relevant rules which extend the Reals appropriately. Similarly 0/0 is meaningless because it represents 0 * (1/0), ie when you divide by X you actually multiple by the number which when multiplied by X gives 1. There is no Y such that Y*0 = 1 in the Reals and therefore 1/0 is no more a valid expression than elephant/cheese = table.

10. ### PeteIt's not rocket surgeryRegistered Senior Member

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Careful, Saint is easily confused.
What eram said true: zero/zero is undefined.

$\lim_{x\to 0}\frac{\sin x}{x} = 1$

$\frac{\sin 0}{0}$ is undefined.

$\lim_{x\to 0}\frac{\sin x}{x}$ is not the same as $\frac{\sin 0}{0}$.

11. ### AlphaNumericFully ionizedRegistered Senior Member

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Exactly, which is why if you define a function $f(x) = \frac{\sin x}{x}$ you have to define the value of f(0) separately. If you decide f(0) = 1 then that fits with the limit but that isn't required.