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Bookmark or Share- Difference between implies and "turnstile" symbols (→ and ⊢)Now 'A implies B' gets used in informal talk both as variant on 'if A then B' and as a variant of 'A logically entails B', i.e. as both what we might regiment as 𝐴→𝐵 and as 𝐴⊢𝐵 [or 𝐴⊨𝐵]. And low and behold, we find being confusingly used both ways [in the object language, or in the metalanguage].
- What does 'imply' mean in maths? - Mathematics Stack ExchangeExamples of such strong assertions are Jammy is both kerplung and zingsty implies that Jammy is not neither kerplung nor zingsty and ∀x (x>5 implies that x>5 or x’ and ‘
- logic - Difference between $\implies$ and $\;\therefore ..."Implies" is completely different. "A implies B" means that IF A is true, then B is also true. It makes no statement about the truth of A. Latex \implies ($\implies$), \Rightarrow ($\Rightarrow$), and \Longrightarrow ($\Longrightarrow$) all give the double right arrow that is often used to mean "implies". Sometimes a single right arrow is used ...
- elementary set theory - Symbol for "if and only if": $\implies$ or ...$$8x + 2x - 44 = 220 + 4 - x \implies 11x = 268 \implies x = 24.36$$ It is legal to use $\implies$ despite of equivalence because you show the direction of your derivation. But, I am not mathematician. And I really find your question interesting. I think that professional proofs use turnstile, ⊢, for your implication instead:
- Implication Logic Truth Table Explained - Mathematics Stack ExchangeA third thing is not to confuse material implication and logical implication : when you say that "A materially implies B" you simply assert that you are, factually, on line (1), or (3) or (4) of the truth table , that is, a situation in which you are not on line (2); this is why ( given the factual truth values in the actual world of the ...
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