# help in interpreting x(t)

I dont know if the wording is confusing but I know x(.) is just $\mathbb{R} \rightarrow \mathbb{R}$. Can I say that as my precise definition.

and then say its just a mapping of real numbers to real numbers. I dont know if its right please help out

“Every magnitude which grows continually but not beyond all limits must certainly approach a limiting value.”

We can interpret “magnitude” as a real number x that changes in time, thus, as a real valued function x(t), t ∈ R. The above sentence is a theorem about the behaviour of such a function as t approaches $\infty$.

(a) The assumptions of the theorem are that the function x(t) is monotone (“grows”) and is bounded (“not beyond all limits”). Give a precise definition of each of these properties of the function x($\cdot$).

(b) State the theorem in your own words.

and also if someone could tell me what this line means

"The side and the diagonal of a square are incommensurable."

like how would i rephrase that if i want to explain this to someone?

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