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answered Does this set tend towards a disc?
comment Any subfield of $\mathbb{C}$ must contain every rational number
@Ritu In short, if yoou do not use induction somewhere in your proof, I'm sure its not correct.
answered $F$ is subfield of complex field $\mathbb{C}$. Show that $F$ is field with characteristic $0$
comment We all use mathematical induction to prove results, but is there a proof of mathematical induction itself?
Once you can define what the set of natural numbers is, I can prove the principle of induction :)
comment Proof check: $(4n)!$ is divisible by $2^{3n}3^{n}$
Induction can hardly be avoided for a function that is defined only by a recursoin.
answered 10 points outside a unit circle
comment Row rank$=$Column rank
Every "output" of $A$ times some vector is a linear combination of the column vectors of $A$.
comment What's the smallest known interval containing at least one prime number?
You mean the asymtotically smallest function $f$ such that there is at least one prime between $x$ and $x+f(x)$ for all (or all sufficiently large) $x$?
comment Why Should $A = \{x | x^2 = 16\ \mbox{and}\ x+6=6\}$ Be An Empty Set?
As a side note, $A$ is not just a null set, i.e., one of possibly many different null sets; there exists exactly one null set and hence $A$ is the null set. Apart from this I prefer the name empty set .
answered Is the graph of $xy=1$ in $\mathbb C^{2}$ connected?
revised Two disjoint compact sets in a topological group
added 15 characters in body
answered Two disjoint compact sets in a topological group
comment Two disjoint compact sets in a topological group
You forgot to reqwuire that $V$ is not empty, I suppose
comment Finding $|E|$, where $E$ is the Splitting Field of $x^8-1$ over a Field of $4$ Elements.
It is well-known that there is no $i$ in team, but there is also no $i$ in characteristic $2$ ...
comment Is every axiom in the definition of a vector space necessary?
@Vim Actually, one axiom is enough: A vector space is an abelian group on which a field acts. :)
comment Find groups that contain elements $a$ and $b$ such that $|a|=|b|= 2$ and $|ab|=5$
@pooja Let $a$ be any reflection, let $c$ be any rotation. Find $b$ such that $ab=c$. Is $b$ a reflection or a rotation?
answered Find groups that contain elements $a$ and $b$ such that $|a|=|b|= 2$ and $|ab|=5$
comment Bounded sequence in a metric space
While this shows that we could base everything on closed balls, we usually argue with open balls only - and be it to avoid that you accidentally use the closed ball of radius $0$.
answered Show that $f(n)$ is $O(g(n))$ then $f(n)+c$ is $O(g(n))$
comment Find all functions f such that $f(f(x))=f(x)+x$
There's no need to assume surjectivity. Injectivity follows readily and your $(4)$ for $a,b>0$ shows (using continuity) that $[0,\infty)$ is in the image. As $x\mapsto-f(-x)$ also has the given property, we conclude that also $(-\infty,0]$ is in the image. (This also shows we need only consider $a>0$)