An Interesting Question

what is the answer of the question? (100-100)/(10-10)

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`2 \times 3`	$2 \times 3$
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Comments

Not exactly "undefined"; a more fitting term would be "indeterminate", because any number $x$ multiplied by zero is zero.

Francis Gerard Magtibay - 8 years, 3 months ago

How to make crazy work: Say $x$ is a number arbitrarily close to $10$ but not exactly $10$ . We need to find $\lim_{x\to 10} \frac{x^2-100}{x-10}=\lim_{x\to 10} x+10=20$

Abhishek De - 8 years, 3 months ago

The main problem with this is that your expression is 'completely arbitrary'. For example, I could say that

$\lim_{x \rightarrow 10} \frac { \frac {1}{2} x^2 + 5x - 100}{ x-10} = \lim_{x \rightarrow 10} \frac {1}{2} x + 10 = 15.$

Adapting this idea, you could arrive at any numerical answer you want. Hence, limits would be unable to resolve this issue, as it is highly dependent on the path that you arrive at the limit.

Note: A similar problem is to define $0^0$ though limits. "Most of the time" we get 1, though if you take $\lim_{x \rightarrow 0} 0^x$ , you will get 0.

Calvin Lin Staff - 8 years, 3 months ago

UNDEFINED

Shourya Pandey - 8 years, 3 months ago

i wish mathematics had something better to offer :/

Harshit Kapur - 8 years, 3 months ago

as from what i learned the real and specific term for 0/0 is INDETERMINATE not undefined

Arlo Andallo - 8 years, 3 months ago

u can not divide anything by zero.