JiminP
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 Sep24 awarded Autobiographer Jul2 awarded Curious May22 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.) May22 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. Apr28 awarded Yearling Mar29 revised How to prove that linear functions cannot represent binary functions Changed = to \in Mar29 asked How to prove that linear functions cannot represent binary functions Mar26 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. Mar25 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. Dec23 comment Is there an uncountable proper subfield of $\mathbf{R}$? Oops... I thought too simply... :( Dec23 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 $(\mathbb{R} \setminus \sqrt{2} \mathbb{Q}) \cup \{0\}$. Dec23 comment What is the meaning of $n\in \aleph$ @arbautjc Thank you! The definition is easier than I thought! Dec23 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 $> \omega$?) Dec23 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. Dec23 answered Calculate the eigenvalues and eigenvectors of matrix $B = A^{4} + 100A^{2} + A + I$ if we know the eigenvalues and eigenvectors of A Dec23 revised largest fraction less than 1 added 437 characters in body Dec23 answered largest fraction less than 1 Dec22 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." Dec22 answered Is this a regular language? Number of a's greater than $k$ Dec22 comment Is this a regular language? Number of a's greater than $k$ I think that's different from "k or more a in w"...