Where $A$, $B$ and $C$ are sets. My doubt is if the notation includes the case $A \neq C$.
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2No, for example ${1}\ne\emptyset\ne{1}$ is a valid statement. – dxiv Apr 25 '23 at 00:18
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14I would regard that notation as ambiguous. If you want to say that the sets are all distinct, say that. Similarly, if you mean to say that $A\neq B$ and $B\neq C$, say that. Writing it this way is sure to cause confusion. – lulu Apr 25 '23 at 00:18
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Perfect, thanks! – smallset Apr 25 '23 at 00:24
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1Personally, I've always read $A\ne B\ne C$ as $A\ne B\land B\ne C$, just like I would not read $x\in A\in \mathcal P(X)$ as $A\cup x\subseteq X\land x\in A$. – Sassatelli Giulio Apr 25 '23 at 01:30
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No. But please avoid this notation when writing, since it can cause this type of confusion. Prefer $A \neq B$ and $B \neq C$ or make clear $A, B, C$ "all different from each other" – tomate Apr 25 '23 at 01:56
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As stated in previous comments, it doesn't. I tried it on Python (which supports this notation), it doesn't... – Nothing special Apr 25 '23 at 02:36
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1@Nothingspecial What Python does is at best vaguely related to how mathematicians read notation. It is not a reliable way to check for the meaning of things. (Though in this case, it agrees.) – Eike Schulte Apr 25 '23 at 05:32
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@EikeSchulte I agree that's true, it's not a reliable way because there might be exceptions. However, Python mostly agrees with usual notations. For example, it evaluates exponent operator from right to left.... – Nothing special Apr 26 '23 at 17:37