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Prove that every type of problem appear in Brilliant!

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Suppose not, then there will be \(0\) problems of some type, say Chemistry.

But then, we would have solve \(0\) problems of Chemistry, which means we solved \(\frac{0}{0}\) of the Chemistry problems. But \(\frac{0}{0}\) is undetermined, which means that \(\frac{0}{0} = x\), where \(x \in \mathbb{R}\).

Thus, we have a contradiction (since the fraction is constant) and thus we have every type of problem in Brilliant. :D

Note by Zi Song Yeoh
4 years, 9 months ago

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9 votes

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What?!

Yang Conan Teh - 4 years, 9 months ago

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?

Zi Song Yeoh - 4 years, 9 months ago

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Nice problem :D

Tan Li Xuan - 4 years, 9 months ago

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But how to solve?

Zi Song Yeoh - 4 years, 9 months ago

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really?

Shourya Pandey - 4 years, 9 months ago

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who says 0/0 is constant? and that it is real?

Harshit Kapur - 4 years, 9 months ago

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0/0 is undefined and is not constant, take for instance the graph of y = x, witch obviously passes through the origin (0;0) on the Cartesian plane. So therefore y/x = 1, therefore every point on the graph will result in one. Therefore if (0;0) lies on the graph, y/x = 0/0 = 1. But now lets examine the grpah of y = -x, witch too passes through the point (0;0). Therefore y/x = -1 and every point on the graph will result in -1. Point (0;0) lies on the graph and therefore y/x = 0/0 = -1. There are infinitely many approaches and slopes that the line can take therefore 0/0 is undefined as it can equal anyone of these values.

Daniel Feinstein - 4 years, 9 months ago

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I didn't say \(\frac {0}{0}\) is constant.

Zi Song Yeoh - 4 years, 9 months ago

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i know, but @Zi Song's statement says that 0/0 = x, x \(\in\) R Since all real are constant, therefore 0/0 is constant this is why i question it. or maybe the R is for something else?

Harshit Kapur - 4 years, 9 months ago

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@Harshit Kapur all reals are constant, but he did not say x is equal to what real or any specific thing.

Yong See Foo - 4 years, 9 months ago

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@Yong See Foo but x is not real! it is undefined

Harshit Kapur - 4 years, 9 months ago

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@Harshit Kapur exactly

Yong See Foo - 4 years, 9 months ago

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dividing by 0 is just absurd. thats it

Yong See Foo - 4 years, 9 months ago

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Please justify the fact that "\( \frac {0}{0} \) is undetermined"

Tim Ye - 4 years, 9 months ago

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0/0 is infinity.

Shubham Kumar - 4 years, 9 months ago

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who said,1/0 is infinity

Sri Venkata Vivek Dhulipala - 4 years, 9 months ago

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