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Aug
26
comment Definition of homeomorphic?
Note that 1. is in fact the literal translation of homeo (ὅμοιος - equal, similar) morph (μορφή - form, shape) ic
Aug
26
comment Will $x=0$ satisfy the equation $\sqrt{\tan(3x)}=\sqrt{-\tan(x)}$?
As this problem seems to come from a "central exam" of the well-known Lomonossov University, it is really a shame that one of the solutions is missing.
Aug
26
answered Is it impossible to recover multiplication from the division lattice categorically?
Aug
26
answered How many combinations are possible, if fare is 50 paisa?
Aug
26
answered Finding a differentiable function from (0,1) to (0,1) dominating (point wise) a given continuous function from (0,1) to (0,1)
Aug
26
comment A Banach Space cannot have a denumerable basis:Why is it true?
The only proper subspace of $\mathbb R$ is $0$ and has empty interior ...
Aug
26
comment A Banach Space cannot have a denumerable basis:Why is it true?
If your book proves this, which step of the proof fails in the case of $\mathbb R$? Could the statement really say "cannot have a countably infinite base"?
Aug
25
comment Roots of $\Phi_{31}(x)$ as roots of unity.
Regarding the last sentence: Just $\zeta^{31}=1$, with equality in $\mathbb F_{32}$. Since $\mathbb F_{32}$ is neither $\mathbb Z/2\mathbb Z$ nor $\mathbb Z/32\mathbb Z$, neither of your modulo suggestions fit.
Aug
25
answered Rolle's Theorem
Aug
25
comment parallel resistors
$f(n)$ is never the empty set, but it may happen that $f(n)$ is not defined. Also, is it on purpose that you map to sets? I.e., one is not allowed to use several identical resistors?
Aug
25
answered Inverse images of ideals
Aug
25
revised How many pairs of natural numbers $(x,y)$, satisfy the equation $\space xy=x+y+\gcd(x,y)$.
edited body
Aug
25
revised How many pairs of natural numbers $(x,y)$, satisfy the equation $\space xy=x+y+\gcd(x,y)$.
edited body
Aug
25
answered How many pairs of natural numbers $(x,y)$, satisfy the equation $\space xy=x+y+\gcd(x,y)$.
Aug
25
comment How to prove that the following sequence will never contains number greater than 3
@stonebrakermatt Put differntly: By definition of the look-and-say process, the $2i$th and the $(2i+2)$th digit are different at any fixed stage. Any block of four or more consecutive digits covers two positions of even index, hence different digits.
Aug
25
accepted If points in a convex set $C$ escape to infinity roughly in direction $v$ then an infinite ray in that direction exists
Aug
25
answered If points in a convex set $C$ escape to infinity roughly in direction $v$ then an infinite ray in that direction exists
Aug
25
awarded  Nice Answer
Aug
25
awarded  functional-analysis
Aug
24
comment Vector space sizes
Let $V$ be the vector space of polynomials and let $T$ be the formal derivative. Then no such $k$ exists.