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Interested in elementary algebra enter image description hereproblems, and teaching.


Jul
13
comment Can an analytic function take a simply connected region to a non simply connected region?
You are right; my answer is the same as yours with less details.
Jul
12
answered Can an analytic function take a simply connected region to a non simply connected region?
Jul
11
answered Eigenvectors of two matrices whose sum is an identity matrix?
Jul
9
answered How to solve $b^2-a^2=d^2-c^2$
Jul
6
answered What kind of transformation an upper triangular matrix represents
Jun
25
comment Find scalars $a$ and $b$ so that $au + bv = (1, −4, 9, 18)$
AS u, v are vectors with 4 components. $xu+yv$ is also of the same kind; equating this with rhs comparing the corresponding parts of vectors gives 4 equations.
Jun
25
answered Find scalars $a$ and $b$ so that $au + bv = (1, −4, 9, 18)$
Jun
25
answered How to establish these two facts about polynomials?
Jun
23
answered Conjugating a permutation
May
29
answered Proving that the following is an exact sequence
May
13
comment Find countable dense subset of $D$, with $D\subset \mathbb{R}\setminus\mathbb{Q}$
I thought we are looking for a countable dense subset of the real line embedded in a given set of irrationals.
May
13
comment Find countable dense subset of $D$, with $D\subset \mathbb{R}\setminus\mathbb{Q}$
@Matt: Any two integral multiples of a real number $x_0$, say $mx_0-nx_0$ differ by at least $x_0$ hence a discrete set (irrespective of $x_0$ being rational or not).
May
13
answered Minimal polynomial of $\sqrt{2}+\sqrt[3]{3}$.
May
13
comment Find countable dense subset of $D$, with $D\subset \mathbb{R}\setminus\mathbb{Q}$
@Matt: See my revised answer.
May
13
revised Find countable dense subset of $D$, with $D\subset \mathbb{R}\setminus\mathbb{Q}$
added 214 characters in body
May
13
comment Find countable dense subset of $D$, with $D\subset \mathbb{R}\setminus\mathbb{Q}$
This set is indexed by a pair of integers, hence countable.
May
13
answered Find countable dense subset of $D$, with $D\subset \mathbb{R}\setminus\mathbb{Q}$
May
9
comment A form of Chinese remainder theorem
In modular arithmetic there is no distinction such as positive and negative numbers; every number is congruent to a positive as well as negative numbers. Take an arithmetic progression: keep subtracting the common difference from the first term and extend it infinitely on the left direction also. Then all the terms of this sequence are congruent to each other modulo the common difference.
May
7
comment Demystify / Solve a number progression.
Of course there is nothing sacred about the solution provided by Lagrange formula: for a sequence like $-1,1,-1,1,-1$ common sense might say next term is $+1$. Bu this formula fitting a 4th degree curve will give something different. The point I wanted to make was any sequence is generatable as polynomial values at equidistant points.
May
7
answered Demystify / Solve a number progression.