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.

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