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 7h answered How to prove $\displaystyle\lim_{x \to 0} \dfrac{\sin^{-1} x}{x} = 1$? 1d answered Is $(A \oplus B)^{\perp} = A^{\perp}\cap B^{\perp}$? 1d answered Contradicting $p|n$s.t $p > \sqrt n$ 2d answered If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$ Apr21 comment Proving by induction on the number of vertices that: every acyclic simple graph is bipartite @y.m.k Erase that vertex. What does P(n) tell you? Apr21 answered Proving by induction on the number of vertices that: every acyclic simple graph is bipartite Apr20 comment Characterizing units in polynomial rings @zed111 In a commutative ring you have unit-nilpotent=unit. The proof is easy: if u is unit and v is nilpotent, then $v^n=0$ which means $$u^n=u^n-v^n=(u-v)(u^{n-1}+u^{n-2}v+...+v^{n-1})$$ This shows that $$(u-v)(u^{n-1}+u^{n-2}v+...+v^{n-1})(u^{-1})^n=1$$ Apr19 comment Error in my proof? As for your last observation, note that $(5^{\frac{1}{\infty}})^\infty$ is indeterminate. Apr19 comment differentiability, complex analysis But if the CR hold for $f^*$, it doesn't necessary mean that $f$ is differentiable. Apr19 answered differentiability, complex analysis Apr18 answered Evaluating $\int_{-a}^{a}\sqrt{a^2-x^2}dx$ Apr17 awarded Enlightened Apr17 answered Show that the set of isolated points of $S$ is countable Apr17 comment Need help with proof of existence of $\sqrt{2}$ How can you say those things before you prove that $\sqrt{2}$ exists? Apr17 comment Albert, Bernard and Cheryl popular question (Please comment on my theory) Because your entire argument is based on understanding what do they DEDUCE. Your argument goes like this: Bernard says something. From here Albert DEDUCES something. From here Bernard DEDUCES something. And from understanding their deductions, we can find the answer. But you wonder if the first step should be exactly what you do at every step in the problem, or if there is some part of dialogue missing.... Apr17 revised Albert, Bernard and Cheryl popular question (Please comment on my theory) added 972 characters in body Apr17 comment Albert, Bernard and Cheryl popular question (Please comment on my theory) In any problem where you have to reason based on a dialog, it is understood that all the dialog is included in the problem... Otherwise, anything can be the answer..... Your case 1 assumes that there is an extra dialog in the problem, which is left out... Apr17 comment Albert, Bernard and Cheryl popular question (Please comment on my theory) The point of this type of the problem is that the people draw conclusions by DEDUCING them from the the given info. And the given info alone. If you start this line of reasoning, that maybe deducing is an assumption, how do you know that Bernard deduced the date from what Albert said...Maybe Albert also told him the month, and the problem didn`t mention it......So how does Bernard knowÉ Apr17 answered Albert, Bernard and Cheryl popular question (Please comment on my theory) Apr17 answered Proving that $\lim_{n\rightarrow\infty}n(a_{n+1}-a_{n})=1 \implies a_n$ diverges to $\infty$