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Questions tagged [quantifiers]

The quantifiers $\forall$ ("for all") and $\exists$ ("there exists") distinguish predicate calculus from propositional logic.

Quantifiers specify the quantity of objects that satisfy a given formula.

The quantifiers $\forall$ (for all) and $\exists$ (there exists) are the most common, but others such as $\exists!$ (there exists a unique) are also in usage.

Only use this tag if your question is about the usage of a quantifier in a formula. Be sure not to use this tag for any question with quantifiers.

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Quantifier question $!\exists x ! \exists y \forall w(w^2>x-y)$

I have a question about the following quantified sentence if it is true or false. $!\exists x ! \exists y \forall w(w^2>x-y)$ for the real numbers I think this this is true because if take two negative numbers $x
Fernando Martinez
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natural language quantifier translation

For the universe of discourse consisting of people, the following natural language translations are intuitive $\forall$ : Everyone $\exists$ : Someone $\neg \forall$ : No one And what about $\neg \exists$? Not-someone? This seems to be the analogy…
doctorjay
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Write using quantifier notation.

"There is one and only one real solution to the equation x^3 + x + 1 = 0" Could someone please explain to me how to write this using quantifier notation?
PSA BITCOIN
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How to prove $\forall x, x^2 \gt x$?

I can't figure out how to prove $\forall x, x^2 \gt x$? I tried substituting $x$ with $2k+1$ and I got $4k^2>-2k$. Besides, I also have problem proving $\forall x,x>1→x^2>x$. Any help will be appreciated.
Zheung Yik
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