Tagged Questions

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Let m ∈ N. Define the relation ≡^ on Z by a ≡^ b for a, b ∈ Z if and only if a ≡ ±b (mod m).

(In other words, the relation ≡^ holds if either a ≡ b (mod m) or a ≡ −b (mod m).) Prove that the relation ≡^ on Z is transitive. ======= I believe there are 3 properties that it must meet ...
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Is my proof ok? Let $m \in \mathbb{N}$. Prove that the congruence modulo $m$ relation on $\mathbb{Z}$ is transitive.

Let $m \in \mathbb{N}$. Prove that the congruence modulo $m$ relation on $\mathbb{Z}$ is transitive. If $A$ is congruent to $B$ mod $m$ then $A - B = k m~~$ (1) If $B$ is congruent to $C$ mod ...
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Is my proof correct? are the arguments right?

my assumptions: (i) $\lim_{t \to \infty}F_{t}(x)=F(x) \ \forall\ x\ \in\ C(F)$(set of continuity points of F) with $F_{t}(x)$ family of distribution functions and $F$ distribution function (ii) ...
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Can someone look at my proof about the convergence of $e^{-tA}$

Hi I am trying to prove that if A is a symmetric positive definite matrix then $e^{-tA}\rightarrow 0$ as $t\rightarrow\infty$. So I have attempted an answer but I'm not sure it is correct. ...