TLA + "Specifying Systems" draft translation --Section 1.4 Formulas and Language (formulas and language)

This section points

• In this book, the formula is a noun can be true or false, this statement is not a statement sentence.

When we first started learning mathematics, the formula is a declarative sentence. formula $2*x>x$ just declarative sentence "Take 2 $x$ ratio $x$ large "short form. In this book, we will enter the realm of logic, this formula is a noun. formula $2*x>x$ is just a formula, it can be true or false, depending on $x$ value of. If we want to declare formula is true, that is, $2*x$ value is really better than $x$ large, we should explicitly write " $2*x>x$ is true. "

Instead of using the formula statement can lead to confusion, on the other hand, the formula is more compact than prose, easier to read. read" $2*x>x$ 2 x multiplied by the value of the big "than reading" than x "is easier, but" $2*x>x$ is true, "may seem a bit redundant so, like most mathematicians, I often write this sentence:

we know $x$ is a positive number, so $2*x>x$。

If a formula is really a statement of whether the formula or the formula is true, the result is not very obvious, then, here's a simple way to tell. This formula is used in place of a name, then read this sentence. If the sentence is grammatically correct, even absurd, then the formula is a formula, otherwise, it is a statement. The above sentence formula $2*x>x$ is a statement, because

we know $x$ is a positive number, so Joe Smith.

This sentence is not grammatical, the following sentence is $2*x>x$ is a formula:

to prove $2*x>x$ , we have to prove $x$ is a positive number.

Because following this stupid sentence is grammatically correct:

In order to prove that John Doe, we have to prove $x$ is a positive number.