JiminP
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 1d awarded Yearling Apr 28 awarded Yearling Sep 24 awarded Autobiographer Jul 2 awarded Curious May 22 comment What are the odds of cracking a cellphone pattern-lock? So can '1-8-2' be done without doing '1-8-5-2'? (My phone can't do this.) And the result 389112 of course concerns those moves. ('1-2-3', '2-1-3', '2-3-1' are valid and different, but '1-3-2' can't be done.) May 22 comment What are the odds of cracking a cellphone pattern-lock? Actually 389112 is correct. It is impossible to draw patterns like '1-8-2' since the middle dot should be also connected. (Swiping fingers like '1-8-1-2' does not help.) I too got 'incorrect' solution 766752 without considering that and got 389112 after fixed. Apr 28 awarded Yearling Mar 29 revised How to prove that linear functions cannot represent binary functions Changed = to \in Mar 29 asked How to prove that linear functions cannot represent binary functions Mar 26 comment Proving two sequences converge to the same limit $a_{n+1}\frac{a_n+b_n}{2} \ , \ b_{n+1}=\frac {2a_nb_n}{a_n+b_n}$ @GinKin Oops. I meant arithmetic mean. Sorry. Mar 25 comment Proving two sequences converge to the same limit $a_{n+1}\frac{a_n+b_n}{2} \ , \ b_{n+1}=\frac {2a_nb_n}{a_n+b_n}$ It seems that $a_{n+1}$ is a geometric mean of $a_n$ and $b_n$, and $b_{n+1}$ is a harmonic mean of same two previous terms. Dec 23 comment Is there an uncountable proper subfield of $\mathbf{R}$? Oops... I thought too simply... :( Dec 23 comment Is there an uncountable proper subfield of $\mathbf{R}$? [This is wrong; I am stupid :(] Simple example: when $x_0 = \sqrt{2}$, the field becomes $(\mathbb{R} \setminus \sqrt{2} \mathbb{Q}) \cup \{0\}$. Dec 23 comment What is the meaning of $n\in \aleph$ @arbautjc Thank you! The definition is easier than I thought! Dec 23 comment What is the meaning of $n\in \aleph$ "Mathematical induction" is usually followed by $\mathbb{N}$, and I think mathematical induction on cardinal numbers $\aleph_1, \cdots$ does not make sense. But I'm not very sure... (By the way, can mathematical induction be done on ordinal numbers $> \omega$?) Dec 23 comment Calculate the eigenvalues and eigenvectors of matrix $B = A^{4} + 100A^{2} + A + I$ if we know the eigenvalues and eigenvectors of A If, $Av = \lambda v$ ($v$ is an eigenvector of $A$ with associated eigenvalue $\lambda$), then: If $i = 0$ or $1$, it's trivial. If $A^i v = \lambda^i v$, then $A^{i+1} v = A A^i v = A \lambda^i v = \lambda^i A v = \lambda^i \lambda v = \lambda^{i+1} v$. Then use mathematical induction. Dec 23 answered Calculate the eigenvalues and eigenvectors of matrix $B = A^{4} + 100A^{2} + A + I$ if we know the eigenvalues and eigenvectors of A Dec 23 revised largest fraction less than 1 added 437 characters in body Dec 23 answered largest fraction less than 1 Dec 22 comment Is this a regular language? Number of a's greater than $k$ Wait, is $k$ decided or undecided? ... I understood the problem as "Amount of a's in w is more than or equals to 2k, where k is a fixed constant."