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12h
revised Do “my” notations already exist or not?
edited title
12h
comment Help me out please with Algebra?
"Teach me X" is simply not what this website is designed for. If you had a specific mathematical question, you can get answers. It's not a question of being "guarded", the point is that the direct, focused Q&A format of this website does not work for what you're looking for.
16h
comment If $H<G$ is a normal subgroup of G,Show that the center $Z(H)$ of H is also normal subgroup of $G$
What are your thoughts? Do you understand the definition of "normal" and "center"?
1d
comment Is there any way to arrive at $\pi$ without mentioning the circle's radius or diameter?
What would it mean to "arrive at $\pi$"? I can produce $\pi$ just by writing down something like $$\pi=4\left(1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\cdots\right)$$ without any reference to a circle at all, does that count?
1d
revised Exponent of an exponent?
edited tags
1d
comment Find all natural numbers *a*, that satisfy the following:
I'll just say this: what can the prime factorizations of the integers $a^2-2a+2$ and $a^2+2a+2$ look like? (By the way, you really have to show your work in future questions. People aren't as inclined to help if you haven't demonstrated any effort or progress yourself.)
1d
answered Find all natural numbers *a*, that satisfy the following:
1d
revised If $F(x) = \frac{1}{2}x(x+1)$, evaluate the following
added 61 characters in body; edited title
1d
comment How is an empty set truly “empty”?
In standard set theory, there is no distinction between "bags" and "marbles". Such a distinction would only make sense with ur-elements.
2d
comment How to find irreducible polynomials in a given ring or field?
None of the elements of the ring $\mathbb{Z}_3[x]/\langle x^2+1\rangle$ are irreducible (and its elements are not appropriately called "polynomials"). An irreducible element of a ring is necessarily not 0 and not a unit, whereas as you have mentioned yourself, the ring $\mathbb{Z}_3[x]/\langle x^2 + 1\rangle$ is a field, so every non-zero element is a unit.
2d
revised Are the integers closed under addition… really?
deleted 3 characters in body
2d
comment Why do both sine and cosine exist?
Why do we have either $\sin$ or $\cos$, when we have the more fundamental $e^x$? $$\sin(x)=\frac{e^{ix}-e^{-ix}}{2i}\qquad\qquad \cos(x)=\frac{e^{ix}+e^{-ix}}{2}$$
Aug
29
reviewed Edit $F$ is subfield of complex field $\mathbb{C}$. Show that $F$ is field with characteristic $0$
Aug
29
revised $F$ is subfield of complex field $\mathbb{C}$. Show that $F$ is field with characteristic $0$
Texed the problem.
Aug
29
revised Why is $(\mathbb{R}, \mathcal{P}(\mathbb{R}))$ called a measurable space when actually is not?
added 1325 characters in body
Aug
29
answered Why is $(\mathbb{R}, \mathcal{P}(\mathbb{R}))$ called a measurable space when actually is not?
Aug
29
comment Is there a mathematical symbol for “and”?
@Jaken: Okay, though I've never heard of such a usage before. What book is this?
Aug
29
answered Is there a mathematical symbol for “and”?
Aug
29
comment Is there a mathematical symbol for “and”?
@Jaken: Unless your goal is to make your mathematics as incomprehensible and annoying as possible, please don't write this sequence of symbols. Common language is far better for communicating to other humans, and is not in any way "less formal" or "less mathematical". I'd far prefer $$\{\text{positive integers}\}\mathrel{\triangle}\{\text{even integers}\} = \{\text{odd positive integers and even non-positive integers}\}$$
Aug
28
comment Prove $R$ is a finite ring
Identically crossposted to MathOverflow: mathoverflow.net/q/215874/1916