# Stavros Mekesis

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# 109 Actions

 Aug6 revised Proper Set Theory Transformation added 4 characters in body Aug6 answered Proper Set Theory Transformation Aug6 comment Set Theory Laws We say that $A$ is a subset of $B$ if every element of $A$ is also an element of $B$. The proper subset is a different thing. If $A$ is a subset of $B$, but $A$ is not equal to $B$, then $A$ is a proper subset of $B$. To prove $(A \cup B \cup C) - (A \cup B) \subseteq (C - A) - B$, let $x \in (A \cup B \cup C) - (A \cup B)$ be arbitrary and then prove $x \in (C - A) - B$. Aug6 revised Set Theory Laws added 2 characters in body Aug6 comment Set Theory Laws I've only proved that $(C - A) - B \subseteq (A \cup B \cup C) - (A \cup B)$ and left the proof of $(A \cup B \cup C) - (A \cup B) \subseteq (C - A) - B$ to you. To prove $(C - A) - B = (A \cup B \cup C) - (A \cup B)$ you must prove both statements. Aug6 comment Set Theory Laws What are $F$ and $G$? Elaborate on this. Aug6 answered Set Theory Laws Aug2 revised If $x^2\equiv 1 \pmod{n}$ and $x \not\equiv \pm 1 \pmod{n}$, then either $\gcd(x-1,n)$ or $\gcd(x+1,n)$ is a nontrivial factor of n added 3 characters in body Aug2 revised Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y| N_2$, you won't get the exact $m$ back when you decrypt $c_2$. Jul27 revised If the same message is sent to Alice and Bob who are using different public keys, how can somoene following the channel find $m$ added 12 characters in body Jul27 answered How do I write a rigorous proof of the following problem: $(A \triangle B) \cup C \neq (A \cup C) \triangle (B \cup C)$ Jul27 awarded Yearling Jul27 revised Proving the properties of big union of unions for indexed sets edited body Jul26 revised Proving the properties of big union of unions for indexed sets deleted 23 characters in body Jul26 revised Proving the properties of big union of unions for indexed sets edited body