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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 $(G, \oplus)$
Apr
21
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?
Apr
21
answered Proving by induction on the number of vertices that: every acyclic simple graph is bipartite
Apr
20
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 $$(u-v)(u^{n-1}+u^{n-2}v+...+v^{n-1})(u^{-1})^n=1$$
Apr
19
comment Error in my proof?
As for your last observation, note that $(5^{\frac{1}{\infty}})^\infty$ is indeterminate.
Apr
19
comment differentiability, complex analysis
But if the CR hold for $f^*$, it doesn't necessary mean that $f$ is differentiable.
Apr
19
answered differentiability, complex analysis
Apr
18
answered Evaluating $\int_{-a}^{a}\sqrt{a^2-x^2}dx$
Apr
17
awarded  Enlightened
Apr
17
answered Show that the set of isolated points of $S$ is countable
Apr
17
comment Need help with proof of existence of $\sqrt{2}$
How can you say those things before you prove that $\sqrt{2}$ exists?
Apr
17
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....
Apr
17
revised Albert, Bernard and Cheryl popular question (Please comment on my theory)
added 972 characters in body
Apr
17
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...
Apr
17
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
Apr
17
answered Albert, Bernard and Cheryl popular question (Please comment on my theory)
Apr
17
answered Proving that $\lim_{n\rightarrow\infty}n(a_{n+1}-a_{n})=1 \implies a_n$ diverges to $\infty$