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Apr
5
reviewed Reopen Expected number of returns by time n in a symmetric 1-d random walk?
Apr
5
reviewed Reopen Proving positivity of the exponential function
Apr
5
reviewed Leave Open Solutions to coupled ODEs
Apr
5
reviewed Leave Open What is the sum of reciprocals of Natural Numbers?
Apr
5
reviewed Leave Open How to simplify $\sum_{i=1}^{k}\binom{n + i - 1}{i}$?
Apr
5
reviewed Leave Open Interesting calculus problems for beginner
Apr
5
reviewed Leave Open How can I prove the following sequence is convergence
Apr
5
revised If the image of a linear transformation of normed spaces is finite dimensional, is the map bounded?
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Apr
5
reviewed Leave Open Trigonometry (sec x)
Apr
5
reviewed Leave Open If the image of a linear transformation of normed spaces is finite dimensional, is the map bounded?
Apr
5
reviewed Leave Open Proving that $\sum_{(m,n)\in \Bbb Z \times \Bbb Z}\frac{1}{m^2+n^2+1}$ diverges.
Apr
5
reviewed Leave Open Combinatorics : number of non-decreasing series of r distinct numbers where the size of series ranges from 1 to N
Apr
5
comment Question based on geomerical properties of complex number.
You have found that $z$ is on the perpendicular bisector of $-iw$ and $i\overline{w}$, and that the two of them are symmetric with respect to the $X$-axis. Therefore, the $X$-axis is their perpendicular bisector. Hence $z$ is on the $X$-axis; $z$ must be real.
Apr
5
comment Question based on geomerical properties of complex number.
Snobbery, that's likely the reason.
Apr
5
comment Proofs of Norms in Quadratic Field
For the case of the quadratic field extension your proof is correct.
Apr
5
comment Proofs of Norms in Quadratic Field
The norm is the determinant of the linear transformation $x\mapsto \alpha x$. Both properties are just the property of determinants $\det(\alpha\beta)=\det(\alpha)\det(\beta)$.
Apr
5
comment Lebesgue nonmeasurable sets
There is a construction due to Sierspinski which you can find in Rudin, page 143. Let $j:[0,1]\to W$ be a bijection with $W$ well-ordered such that $j(x)$ has only countably many predecessors, for $x\in[0,1]$. Take $E$ to be the points $(x,y)\in[0,1]^2$ such that $j(x)< j(y)$. To see non-measurability, check Fubini's theorem for its characteristic function.
Apr
5
revised Lebesgue nonmeasurable sets
added 13 characters in body
Apr
5
comment Find norm in $\mathbb Q[\sqrt{5}]$
It is the product of the roots of the minimal polynomial raised to the power of the degree of the field extension [L:\mathbb{Q}(\sqrt{5})], where $L$ is the field that you are considering. In your case $L=\mathbb{Q}(\sqrt{5})$. So, $[\mathbb{Q}(\sqrt{5}):\mathbb{Q}(\sqrt{5})]=1$.
Apr
5
comment Find norm in $\mathbb Q[\sqrt{5}]$
Yes, that's right.