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comment Determining the derivative of $e^{5x}\tan(2x)$
shouldn't $g(x) = \tan(2x)$?
May
30
comment product of two ideals
@Andrew As an example, $2\mathbb{Z} + 3\mathbb{Z} = \mathbb{Z}$ because we can write $1 = 4 + (-3)$ and the first summand belongs to $2 \mathbb{Z}$ and the second one belongs to $3 \mathbb{Z}$. On the other hand, $4\mathbb{Z} + 6 \mathbb{Z} \neq \mathbb{Z}$. Any element of $4 \mathbb{Z} + 6\mathbb{Z}$ is of the form $4x+6y$ for some integers $x,y$; in particular, it is always even so it can never be equal to $1$. I hope this helps.
May
30
comment product of two ideals
@Andrew But $I+J = R$ is a condition on $I$ and $J$! In general, $I+J$ is an ideal of $R$ which may or may not be equal to $R$.An equivalent way to state this condition is that $1 = i + j$ for some $i \in I$ and some $j \in J$. That is, $I+J=R$ if and only if you can write $1$ as a sum of an element of $I$ and an element of $J$.
May
29
comment product of two ideals
@Dylan Moreland: Thanks for your comment! I just edited my answer.
May
29
revised product of two ideals
deleted 21 characters in body
May
29
answered product of two ideals
May
29
answered Simple Set Theory Question
May
28
comment Duality of $L^p$ and $L^q$
@t.b. Thank you for your comment and for the link. I appreciate it.
May
28
answered Duality of $L^p$ and $L^q$
May
27
answered Is this $\left|\left(\frac{a}{b}\right)^n-\left(\frac{a}{b}\right)^{n-1}\right|$ bounded?
May
20
comment Is the determinant of a matrix lower when all its elements are lower?
If $A$ and $A'$ are stochastic, then $A = A'$ as Marvis showed in the response above.
May
20
comment Is the determinant of a matrix lower when all its elements are lower?
It looks like we came up with the same example:-)
May
20
answered Is the determinant of a matrix lower when all its elements are lower?
May
18
comment If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field.
Yes, you are correct!