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Apr
24
comment What is the maximum value of $\int_{0}^{2}{h(t)}dt$?
welcome to MSE. Please note this is not a good way to pose a question here. What is the purpose of you asking this question here? What have you tried? Where are you stuck? You have to be clear about these things if you want to get helpful answers.
Apr
17
comment Limit point symmetric?
Assuming your interpretation of $x$ is a limit point of $y$ is that $x$ belongs to the closure of $\{y\}$, the answer is that in an arbitrary topological space $X$ the relation $x\in Cl(y)$ need not imply $y\in Cl(x)$, as is very well-known. Very minimal separation conditions do imply the implication, as is also very well-known.
Apr
16
comment Is set membership relation a set?
If the set of all sets exists (call it $U$), then the membership relation is the set $\{(x,y)\in U\times U\mid x\in y\}$. So if the set theory you work with allows for the constructions needed for this definition of a set, then you're done.
Apr
14
comment Why isn't '&' used for logical conjunction?
@Constantine just like painting is not about brushes, but a question about a new style of brush certainly is of interest and belongs to world of painting, so is mathematics not about notation, but a question about some notational style is of interest and belongs to the world of mathematics.
Apr
14
comment Why isn't '&' used for logical conjunction?
you may wish to correct the year for Peano. I doubt he practiced mathematics in 1988....
Apr
12
comment closed union of closed sets
Would anything go wrong if one takes the upper Vietoris topology? or the Vietoris topology?
Apr
12
comment Proof that $0^0 \neq 1$
what is your definition of $0^0$?
Apr
12
comment closed union of closed sets
I'm interested in a convenient formalism for upper/lower semicontinuous functions, primarily in the context of generalised inverse limits of compacta (and generalisations thereof).
Apr
12
comment closed union of closed sets
Yes @StuKraji do you have a good reference?
Apr
8
comment why can't quintics be solved by radicals and the relevance of permutations of roots of polynomials
perhaps you would like to read Galois' original text as well.... Joking aside, the modern treatment through Galois theory is an enormous simplification over any of the original treatments. Tackling, say, Abel's work directly is going to be extremely challenging, while there are several excellent books that go from nothing to the Galois correspondence in under 150 pages, complete with all the linear algebra and group theory prerequisites, and applications not only to the insolubility of the quintic, but (why not, it's so easy once you have Galois) other famous results.
Apr
3
comment How many quadratic extension are there on a field?
Do you think that $\mathbb Q (\sqrt 2) $ is isomorphic to $\mathbb Q (\sqrt 3)$? Try to construct an isomorphism.
Mar
29
comment Why is cardinality of set of even numbers = set of whole numbers?
@nxs responding to your comment to me, you seem to confuse abstract with arbitrary. There is nothing arbitrary in the choice of axioms for the things we study, no matter how abstract or concrete they are.
Mar
29
comment Why is cardinality of set of even numbers = set of whole numbers?
@nxs your confusion stems from trying to think of cardinal equality in geometric terms. That simply can not be done since by its very definition cardinal equality is about abstract sets, devoid of any geometry. You got confused because you consider sets for which you have a concept of geometry for, and you forgot to neglect it since you are only concerned with cardinality.
Mar
22
comment Why study dimensions?
measures 'count' side in a different way. The rationals for instance are countable, so are small relative to the reals, i.e., they have measure 0. But the closure of the rationals are the reals, so in that respect they are large with respect to the reals, i.e., they are dense. Size matters, and size may change according to perspective.
Mar
15
comment noncommutative ring with unity..
is any of the sets you describe closed under addition and multiplication? (hint: no!).
Mar
13
comment The distance between disjoint closed sets may be zero
Welcome to MSE. This is not a drop-your-homework-on-us type site. What have you done to try and solve this problem? where did you get stuck?
Mar
13
comment How to call a mathematical space “$(\mathcal S, f)$” consisting of set $\mathcal S$ and function $f : \mathcal{S \times S} \rightarrow \mathbb R$?
Good luck!! If you can obtain interesting results about these 'spaces', then you can post some of your results and motivation, and seek ideas for a name. At this point, it's an unborn baby, one that was not even conceived yet. Don't get too attached to it.
Mar
13
comment Is it possible to prove uniqueness without using proof by contradiction?
@MathematicsStudent1122 certainly, though that is an overkill as it follows easily by elementary properties of the reals.
Mar
13
comment Is it possible to prove uniqueness without using proof by contradiction?
It would be if you provided a proof of the injectivity of the function that does not use contradiction. Right now, all you stated is a tautology. You did not prove anything. Moreover, you say "we use the injectivity property" but then you go ahead and seem to deduce the injectivity of the function". It is not clear what you are trying to do in this answer.
Mar
13
comment Is it possible to prove uniqueness without using proof by contradiction?
yes, well, that is a tautology. How does that address OP's question?