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Sentence (mathematical Logic)




For example

:( \exists x)x^2=y

is ''not'' a sentence, because of the presence of the free variable y; it will be true in the structure of the Real Number s if y=2, but not if y=-2. On the other hand

:( orall y)(\exists x)x^2=y

''is'' a sentence, and is false in the real numbers.