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    I learned that $\models$ stands for semantic entailment, while $\vdash$ stands for provability in a certain proof system More concretely: Given a set of formulas $\Gamma$ and a formula $\varphi$ in some logic (e g , first-order logic), $\Gamma \models \varphi$ means that every model of $\Gamma$ is also a model of $\varphi$ On the other hand, fix a proof system (e g , sequent calculus) for
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    I was reading a paper about well-orderings and this came up: Suppose (E, ≤) and (F, ≼) are isomorphic well-orderings Then there exists a unique isomorphism for (E, ≤) to (F, ≼) I've been scouri
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    I have started seeing the "∈" symbol in math What exactly does it mean? I have tried googling it but google takes the symbol out of the search
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    The dot product tells you what amount of one vector goes in the direction of another For instance, if you pulled a box 10 meters at an inclined angle, there is a horizontal component and a vertical component to your force vector So the dot product in this case would give you the amount of force going in the direction of the displacement, or in the direction that the box moved This is
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    It's worth mentioning the distinction between "coprime" and "relatively prime": A set of integers is relatively prime if no integer > 1 divides all of them an example being (3, -7, 1) A set of integers is "coprime" if no integer > 1 divides any pair of them So for two integers the two definitions coincide, but for more than two the property of "coprimeness" is stronger, because for example a
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    Other symbols I have seen used for "is defined to be equal to" are three horizontal lines instead of two, and $=$ with either a triangle or "def" written directly above it I have seen variants of these used by people who predate widespread knowledge of computer programming It would be interesting to know the earliest uses of a special symbol for this (and what symbols were chosen) An
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    I am helping with homework I am stumped here - What is the meaning of the small round circle, or small "o" in question 19 (that I underlined) and question 20





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