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seen Dec 7 at 21:45

Jan
15
comment Is $f = x^2$ or only $f(x) = x^2$ correct?
if, by $x$, the /variable/ is meant, then I do not see how that would be incorrect. You are right however, that (in words) "plugging in a value" produces a new "value".
Jan
15
comment Is $f = x^2$ or only $f(x) = x^2$ correct?
So why is your view correct? Under my view, the notation is correct (albeit confusing, since I am leaving away all the isomorphisms), but under your view, it is not.
Jan
15
comment Is $f = x^2$ or only $f(x) = x^2$ correct?
Not quite - $x$ is not some value, but instead a variable. In that case, $x^2$ can be seen as an element of $\mathbb{R}[x]$, the ring of polynomials, which is isomorphic to a subset of the ring of continuous functions.
Jan
8
comment Mathematics, Philosophy and writing.
Perhaps more famous for his literature than his mathematics: Charles Dodgson / Lewis Caroll.
Jan
5
comment Learning category theory before abstract algebra
I think categories inherently have group-like properties, so I'd suggest you learn abstract algebra first. Though strictly speaking, neither relies on the other, so you can give it a shot.
Jan
5
comment In a ring homomorphism we always have $f(1)=1$?
Could you add a word on why we want to rule out such mappings?
Jan
5
answered In a ring homomorphism we always have $f(1)=1$?
Jan
2
comment a problem on the topological properties of a annulus
Please fix ambiguous terminology: to say a map is open or closed usually refers to its graph having such properties.
Jan
2
comment Are there real-life relations which are symmetric and reflexive but not transitive?
Surely this relation is not reflexive for newborns...
Dec
31
suggested rejected edit on Do eigenvectors always form a basis?
Dec
29
comment How to prove that something is definable or not definable in a given structure?!
Dear André, I am currently doing a little undergraduate research project in o-minimal structures. Thank you for showing me that this is actually something more people know about :P
Dec
28
comment A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language
This theorem would fail Feynman's judgement for the same reason that Banach-Tarski is not an example.
Dec
27
comment Consider the sequence 01110100…
Induction?[filler]
Dec
26
comment The cardinality of $\mathbb{R}/\mathbb Q$
Awesome.[filler]
Dec
26
comment The cardinality of $\mathbb{R}/\mathbb Q$
So why exactly are they both size continuum?
Dec
25
comment Rouche's theorem
So... what did you try?
Dec
24
comment Studying Math, All Over Again
With all due respect, Khan is not mathematics. Khan is a list of courses in passing exams.
Dec
23
comment Finding $\lim_{x\to \pm\infty}f(x)$ where $a,b>0$
It's bounded from above by $(a+b)/2$
Dec
23
reviewed Reviewed Orthogonal set vs. orthogonal basis
Dec
23
reviewed No Action Needed Formula for 12 days of Christmas?