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Apr
13
answered Prove that f(X) is constant.
Apr
13
comment Prove that f(X) is constant.
I don't know what you mean by, "I have seen a lot of answers around here which seem to be good enough." Do you mean you have posted this question here before?
Apr
12
comment Besides Vandermonde matrix, is there any other $m$ by $n (m>n)$ matrix in which any $n$ rows has a full rank?
Consider an $n\times n$ submatrix. Compute its determinant by expanding along the first row. You get a linear combination of the entries of the first row being zero, but the elements in the first row are linearly independent over the field generated by the other entries, so all the coefficients must be zero. The coefficients are order $n-1$ determinants, so we win by induction on $n$.
Apr
12
comment Prove that the following relation is an equivlance relation.
Start with $a=1$. Test $b=1,2,3,\dots$ to see which ones are in the equivalence class of $a$. When you see a pattern, stop computing, and prove the pattern works. Then take the smallest integer not in the class of $1$, and repeat the experiment. Eventually, you will get the idea and you will know how many equivalence classes there are.
Apr
12
answered Series formed by reciprocal of fixed points of a function
Apr
12
answered Besides Vandermonde matrix, is there any other $m$ by $n (m>n)$ matrix in which any $n$ rows has a full rank?
Apr
12
comment Determine and prove if the following are equivalence relations, partial ordering relations, or neither.
Well, give it a shot --- can you decide whether the first one is reflexive? It really helps if we know what you can do on your own. Also, I think you're missing something in the 3rd one, maybe $b\equiv0\pmod a$.
Apr
12
awarded  modular-arithmetic
Apr
12
awarded  Nice Answer
Apr
11
comment Galois theory Radical extension
@arbautjc, good sleuthing, bad spelling.
Apr
11
comment How many $3$-subsets of $\{1,2,\ldots,10\}$ contain at least one even and one odd integer?
@analysis89, I think you are misunderstanding the problem. Suppose the question didn't have the "such that" part. Then the answer would be the number of ways of choosing 3 things from 10, that is, the binomial coefficient 10-choose-3. We're not partitioning the set into 3-element subsets; we're counting the total number of 3-element subsets that exist.
Apr
11
comment Galois theory Radical extension
Please cite your source, your reason for interest in the question, what you know about the question, where you get stuck, and so on. Also, please write "$K$ over $F$" instead of $K=F$, unless you really mean $K=F$.
Apr
11
answered Why is an irrational number's algebraic complexity the opposite of its Diophantine complexity?
Apr
11
comment How many $3$-subsets of $\{1,2,\ldots,10\}$ contain at least one even and one odd integer?
I don't know why you are distributing numbers to three sets. The question is about three-element sets, and how many different ones there are.
Apr
11
answered Show that every subspace of $\mathbb{R}^n$ is a kernel of a linear map.
Apr
11
comment Find $x,y$ such that $x=4y$ and $1$-$9$ occur in $x$ or $y$ exactly once.
My idea would be to program a computer to do it for you. There aren't that many 4-digit numbers.
Apr
11
comment Group action on subsets
@099, if what you meant isn't what you asked, then you should edit your question so it reflects your intended meaning.
Apr
10
comment Proving Post Correspondence Decidable
Maybe you could remind us --- what is the Post Correspondence Problem?
Apr
10
comment Group action on subsets
@Babak, I don't know what you mean by $\Omega$, nor by $\omega$.
Apr
10
comment Group action on subsets
For an example of size 3 in $D_3$, which I prefer to think of as $S_3$, let $S=\{{(12),(13),(23)\}}$. Then $S$ is not a subgroup, but $(12)S=(13)S=(23)S$.