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# Prove that every type of problem appear in Brilliant!

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, 6 months ago

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What?! · 4 years, 6 months ago

? · 4 years, 6 months ago

Nice problem :D · 4 years, 6 months ago

But how to solve? · 4 years, 6 months ago

really? · 4 years, 6 months ago

who says 0/0 is constant? and that it is real? · 4 years, 6 months ago

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. · 4 years, 6 months ago

I didn't say $$\frac {0}{0}$$ is constant. · 4 years, 6 months ago

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? · 4 years, 6 months ago

all reals are constant, but he did not say x is equal to what real or any specific thing. · 4 years, 6 months ago

but x is not real! it is undefined · 4 years, 6 months ago

exactly · 4 years, 6 months ago

dividing by 0 is just absurd. thats it · 4 years, 6 months ago

Please justify the fact that "$$\frac {0}{0}$$ is undetermined" · 4 years, 6 months ago

0/0 is infinity. · 4 years, 6 months ago