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29m
comment Greatest Common Divisor of two binary polynomials
(1) In your question you wrote $x^4+x^3+x^2+1$ which is not irreducible. If you meant $x^4+x^3+x^2+x+1$ (which is irreducible) you should edit the question. (2) If $f(x)$ is irreducible, then the GCD of $f(x)$ and $g(x)$ is either $1$ or $f(x)$. So you only need one division to find out if $g(x)$ is divisible by $f(x)$, i.e., the first step of the Euclidean algorithm. (3) Of course the Euclidean algorithm will find the GCD without knowing anything about the irreducibility or factorization of either of the polynomials. If this is an exercise on the Euclidean algorithm you should use it.
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revised Monotone Sequence of Sets
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comment Why do we care about non-$T_0$ spaces?
You are probably right about pure topology. In applied topology, pseudometrics arise naturally, e.g. in function spaces. Of course you can make them metric spaces by taking a quotient, but maybe it's more natural to think of the "points" as functions rather than equivalence classes of functions.
4h
comment Sequence Lemma explanation
Definition are part of math. Understanding the definitions is a good start to understanding math.
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comment Sequence Lemma explanation
Duh, thanks. I know what convergence of a sequence means. It think for jip to write out the definition in words would be a good start to understanding why the greyed line is true. It is pretty much immediate from the definition.
5h
comment Sequence Lemma explanation
Yes, I know. What does "$x_n$ converges to $x$" mean? Definition?
5h
comment Sequence Lemma explanation
what does $x_n\to x$ mean?
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comment Sequence Lemma explanation
What's your question?
7h
comment Greatest Common Divisor of two binary polynomials
If you know that one of the polynomials is irreducible, that narrows down the answer quite a bit, doesn't it?
7h
comment Does it take a genius to do mathematics/physics on a university level?
@Nameless If I have seen less far, it is by standing in the footprints of giants.
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revised A conjecture in equational logic
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answered Existence of a countable $\sigma$-algebra on an uncountable set
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revised A conjecture in equational logic
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revised A conjecture in equational logic
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comment A conjecture in equational logic
More generally (and closer to your original question), is there a single identity which implies the commutative and associative laws, without implying that the operation is a constant function? For that matter, do you know of a single identity, other than the commutative law itself, which implies the commutative law but does not imply that the operation is constant?
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answered Prove that $G$ has at least $q-p+c$ cycles.
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answered List one of the ways in which Mario could buy the stars and comets. Note: Mario needs to spend all of his gold coins
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comment Clueless when solving recurrence relations
It's a good idea to find $T_h$ first. That's how you know to use $T_p=n(An+B)$ instead of $T_p=An+B$.
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answered All possible types of permutation.
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revised discrete math: properties of a relation
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