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515
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location Daejon, South Korea
age 19
visits member for 3 years, 4 months
seen 23 hours ago

asdf


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."
Dec
22
answered Is this a regular language? Number of a's greater than $k$
Dec
22
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"...
Dec
18
answered How many solutions are there?