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Jan
22
reviewed Leave Open How prove that $|y-x|\le \frac 1n$ implies $|f(y)-f(x)|\le \frac1n|f(1)|$?
Jan
22
reviewed Leave Open What are the integer values of $\frac {8 + 4 \cdot 3^{a}+2 \cdot 3^{a+b}+3^{a+b+c}} {3^{a+b+c+d} - 16}$?
Jan
22
reviewed Leave Open How should I calculate the $n$th derivative of this expression?
Jan
22
reviewed Close The Three Subjects
Jan
22
revised Proving $proj_{proj_{\vec u} \vec v} \vec v=proj_{\vec u} \vec v$
added 143 characters in body
Jan
22
awarded  Notable Question
Jan
7
comment Prove that $\frac{a}{\sqrt{a^2+1}}+\frac{b}{\sqrt{b^2+1}}+\frac{c}{\sqrt{c^2+1}} \leq \frac{3}{2}$
What is the meaning of the symbol $\sum_{cyc}$?
Dec
28
revised Prove that $5^n + 2\cdot3^{n-1} + 1$ is multiple of $8$
added 83 characters in body; edited tags
Dec
16
comment Tentative proof of Poincaré-Miranda theorem?
@DanielFischer I will improve my argument and edit my attempt proof. Thank you for your comments.
Dec
16
comment Tentative proof of Poincaré-Miranda theorem?
@DanielFischer I hope this argument is correct. Otherwise I'll edit my attempt proof.
Dec
16
comment Tentative proof of Poincaré-Miranda theorem?
@DanielFischer The equality involving the limit above $\lim_{k\to \infty}f_2\bigl(u_1^{\ast}(u_2^k,x_3,\dotsc,x_n), u_2^k,x_3,\dotsc,x_n\bigr)=f_2\bigl(u_1^{\ast}(\tilde{u}_2^,x_3,\dotsc,x_n), \tilde{u}_2,x_3,\dotsc,x_n\bigr)=0$ implies continuity of $u_2 \mapsto f_2\bigl(u_1^{\ast}(u_2,x_3,\dotsc,x_n), u_2,x_3,\dotsc,x_n\bigr)$.
Dec
16
comment Tentative proof of Poincaré-Miranda theorem?
@DanielFischer I refer the function $(x_2,\ldots, x_n)\mapsto u_1(x_2,\ldots, x_n)$. But about the function $u_2 \mapsto f_2\bigl(u_1^{\ast}(u_2,x_3,\dotsc,x_n), u_2,x_3,\dotsc,x_n\bigr)$ for all sequence $\{u^k_2| f_2\bigl(u_1^{\ast}(u_2,x_3,\dotsc,x_n), u_2,x_3,\dotsc,x_n\bigr)=0\}$ such that $u_2^k\to \tilde{u}_2$ we have $\lim_{k\to \infty}f_2\bigl(u_1^{\ast}(u_2^k,x_3,\dotsc,x_n), u_2^k,x_3,\dotsc,x_n\bigr)=f_2\bigl(u_1^{\ast}(\tilde{u}_2^,x_3,\dotsc,x_n), \tilde{u}_2,x_3,\dotsc,x_n\bigr)=0$.
Dec
16
comment Tentative proof of Poincaré-Miranda theorem?
@DanielFischer If we observe the argument, the continuity of $u_1^\ast( x_2,\ldots, x_n)$ is irrelevant. Note that we have $f_1(u_1(x_2,\ldots,x_n),x_2,\ldots,x_n) =0\;\forall x_2\in[a_2,b_2],\;\forall x_3\in[a_3,b_3],\ldots,\;\forall x_n\in[a_n,b_n]$.
Dec
15
comment Tentative proof of Poincaré-Miranda theorem?
@DanielFischer, Fixed $u_1^*$ the function $u_2\mapsto f_2(u_1^*,u_2,x_3,\ldots,x_n)$ continuously depends only on $(u_2,x_3,\ldots,x_n)$ once the $f$_2 function is continuous in its 'n' coordinates, which will also be continuously follows the 'n-1' remaining coordinates.
Dec
15
revised Tentative proof of Poincaré-Miranda theorem?
Correcting a small mistake of notation.
Dec
15
comment Tentative proof of Poincaré-Miranda theorem?
@Alex, "But it may be that ff has a 0 that cannot be solved algebraically, so its existence won't so easily follow from the IVT". But the conclusion of existence of IVT not depend on any algebraic construction.
Dec
15
revised Tentative proof of Poincaré-Miranda theorem?
Minor errors.
Dec
15
reviewed Approve Find transitive relations
Dec
15
reviewed Reject Proof Check in Algebra
Dec
15
asked Tentative proof of Poincaré-Miranda theorem?