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Apr
7
comment $\varepsilon$-$\delta$ proof of continuity of floor function $\lfloor x\rfloor$
How could you even think that the floor function is everywhere continuous?
Apr
7
comment Arc subtended by inner infinitesimal angle
My first suggestion is that you draw a comprehensible figure.
Apr
7
comment Verifying proof that $f$ has an inflection point at zero if $f$ is a function that satisfies a given set of hypotheses.
Your argument is correct. What is not so correct, and makes your question difficult to understand, is the presentation of the hypotheses for $f$.
Apr
6
comment Find all Real polynomials.
Missing is an argument of the following kind: When $f_1$ and $f_2$ are two solutions of the problem then $f_1-f_2$ has to be zero at $x\in\{2,3,5\}$. Therefore $f_1(x)-f_2(x)=(x-2)(x-3)(x-5) g(x)$ for some polynomial $g$.
Apr
6
comment the relationship between $f^{-1}(x)$ and $x$
Use another letter, as $y$, for numbers in the range of $f$, i.e., in the domain of $f^{-1}$. Note that the subset $f^{-1}(\{y\})\subset\ ]0,1[\ $ is defined even if $f$ is not injective, and $x>y$ holds for all $x$ in this subset.
Apr
6
comment Cosine of an area
Now you have it right!
Apr
5
answered Calculate $\sqrt{5}$ using taylor series to the accuracy of 3 digit after the point $(0.5*10^{-3})$.
Apr
5
comment Has lack of mathematical rigour killed anybody before?
This is not about "mathematical rigour" but about wrong thinking.
Apr
5
comment Cosine of an area
What "can be easily proved" is wrong: The scaling factor for segments depends on their direction. Segments $\sigma\subset B$ orthogonal to $g:=A\wedge B$ are scaled by a factor $\cos\theta$, and segments parallel to $g$ keep their length under projection. Now find out how the area of suitable rectangles is scaled. It is a nontrivial theorem that all areas are scaled by the same factor.
Apr
5
answered Trick with differentials from $\frac{dr}{ds} \to \frac{dr}{dt}$
Apr
5
comment What does the sign “$=$” exact meanings?
Thank you for the quote!
Apr
5
comment Identical objects into identical boxes
This question is a duplicate. There is an accepted answer here: math.stackexchange.com/questions/1219692/…
Apr
5
comment My try at the completeness axiom proof
It's unclear what you assume about ${\mathbb R}$, and what you want to prove.
Apr
5
answered Proving positivity of the exponential function
Apr
5
comment Proving positivity of the exponential function
Put $x:=-20$ in your second displayed formula!
Apr
5
comment Having difficulty understanding topological groups.
Nondiscrete topologies on finite sets are a nightmare. Basic examples of topological groups are $({\mathbb R},+)$, ${\mathbb R}_{>0},\times)$, $S^1$, $GL(n,{\mathbb R})$.
Apr
4
revised $12$ Identical balls can be placed into $3$ identical boxes,
added 23 characters in body
Apr
4
revised If $\lim_{x\to0} f(x)+g(x)$ and $\lim_{x\to0} f(x)g(x)$ exist simultaneously, are there any $f(x)$ and $g(x)$ that do not have limit
added 62 characters in body
Apr
4
answered Showing that the function $f(x,y)=x\sin y+y\cos x$ is Lipschitz
Apr
4
revised Jacobian matrix dimension problem?
added 515 characters in body