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Jul
15
accepted prove that $ A^k$ is diagonalizable
Jul
15
accepted How to show that $\gcd(a,b) = ax+by \implies \gcd(x,y)=1$?
Jul
15
accepted How to find $\gcd(f_{n+1}, f_{n+2})$ by using Euclidean algorithm for the Fibonacci numbers whenever $n>1$?
Jul
15
accepted Let a|c and b|c such that gcd(a,b)=1, Show that ab|c
Jul
15
accepted Show that every prime $p>3$ is either of the form $6n+1$ or of the form $6n+5$
Jul
15
accepted How to prove by induction that $a^{2^{k-2}} \equiv 1\pmod {2^k}$ for odd $a$?
Jul
15
accepted How to show that integers $x_0+\frac{m}{d}t$, $t = 0, 1,…, d-1$, are pairwise incongruent modulo m.(Hint! Antithesis.)?
Jul
15
accepted How do you get possible candidates for primitive roots of 12?
Jul
15
accepted How to solve $x^3=-1$?
Jul
15
accepted How to show that $f-g$ is imaginary constant in $\mathbb{D}$?
Jul
15
accepted How to show that if $f$ or $g$ is continuous, then the convolution $f \star g$ of those functions is continuous?
Jul
15
accepted How to show by example that existence of barrier function of any set $U\subset \mathbb{C}$ is dependent of its set?
Jul
14
accepted How you'd show that $f$ is not continuous?
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
30
comment How to show that if möbius transformation has an inverse, then it is injective?
But if you have $f(x)=x^2$(counter example) then $-1=a\neq b=1$, but still although $f$ has an inverse $f^{-1}=\sqrt{x}$, still $f(-1)=f(1)$. Am I missing something, if you know what I mean?
Jun
30
comment How to show that if möbius transformation has an inverse, then it is injective?
Ok. I would like to know how to show injectivity of a function $f(x)$ which has an inverse $f^{-1}$ by proving instead using contrapositive of $f(x)=f(y) \Rightarrow x=y$. I mean how to prove that $f$ is injective if $\exists f^{-1}$ such that $f^{-1}\circ f = Id_A$ and $f \circ f^{-1} = Id_B$ and you use definition of injectivity where $x\neq y \Rightarrow f(x)\neq f(y)$. I tried to prove injectivity of $f$ by using $x\neq y \Rightarrow f(x)\neq f(y)$, but did not managed to do that.
Jun
30
comment How to show that if möbius transformation has an inverse, then it is injective?
Well I just ask hint of how to prove injectivity of $f$ by using $a\neq b \Rightarrow f(a)\neq f(b)$ with assumptions given at the beginning of my question?
Jun
30
comment How to show that if möbius transformation has an inverse, then it is injective?
Is it possible to proof injectivity of $f$ by using this( $a\neq b \Rightarrow f(a) \neq f(b) $)? I could not find a way to proof injectivity in above way.
Jun
26
accepted How to show that if möbius transformation has an inverse, then it is injective?