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- abstract algebra - $K$ is a splitting field $\iff$ any irreducible . . .
Let $K F$ be a finite extension I want to show that $K$ is a splitting field over $F$ $\iff$ any irreducible polynomial $p (x)\in F [x]$ that has a root in $K
- abstract algebra - If $G Z (G)$ is cyclic, then $G$ is abelian . . .
@Robert: Yes, I think so Where did the negative exponent come from? Would you want to make this comment a formal "answer"?
- radicals - Is there a way to check if an integer is a square . . .
Is there a way to check if a number is square number? For example, we know that $4$ is a square number because $2^2=2$ and $9$ is a square number because $3^2=9$ But for example $5$ is not a square
- Integrated Circuit: Definition, Formula, Derivation and Examples - Toppr
An integrated circuit refers to a chip that contains various interconnected multiple electronic components Furthermore, the location of this chip is on a semiconductor material and it contains both passive and active components
- If $φ:I→J$ is a homeomorphism then $f_n→f$ implies that $ (f_n∘φ) → (f∘ . . .
If $φ:I→J$ is a homeomorphism then $f_n→f$ implies that $ (f_n∘φ) → (f∘φ)$ with respect the uniform, pointwise and $L_2$ topology respectively?
- If $f$ and $g$ are surjective, then $g (f (x))$ is surjective
What part of the proof are you having trouble understanding? In my reading, the image you posted contains a complete and detailed proof directly from the definition of surjective
- Mutually Singular measures - Mathematics Stack Exchange
(ii) $\int_Ig_ndm=1$ for all $n$, (iii) $\lim_ {n\to\infty}\int_Ifg_ndm=\int_Ifd\mu$ for every $f\in C (I)$ Does it follow that the measures $\mu$ and $m$ are mutually singular? I know that $\mu$ and $m$ are mutually singular if they are concentrated in different disjoint sets, but how do I connect that with the 3 properties above?
- discrete mathematics - Is empty set an element of a set . . .
The empty set is a subset of every set including itself, but it is not necessarily an element of any particular set
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