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Languages evolve to make essential ideas easy to express.

The language of mathematics makes it easy to express
the kinds of thoughts that mathematicians need to express.


It is:

PRECISE (able to make very fine distinctions):
compare [beautiful math coming... please be patient] $\,5x^2\,$ and $\,(5x)^2\,$

CONCISE (able to say things briefly):
the expression [beautiful math coming... please be patient] $\,3x^2 - 5x + 7\,$ represents this sequence of operations:
take a number, square it, multiply it by $\,3\,,$ subtract five times the original number, then add $\,7\,$

POWERFUL (able to express complex thoughts with relative ease):
It takes a full week of classes to fully flesh out this statement, which is the central idea in Calculus:
[beautiful math coming... please be patient] $$ \begin{gather} \lim_{x\rightarrow c} f(x) = \ell\cr \text{ is equivalent to }\cr \forall\ \ \epsilon \gt 0\ \ \exists\ \ \delta \gt 0\ \ \text{s.t. if}\ \ x\in\text{dom}(f)\ \ \text{and}\ \ 0 \lt |x - c| < \delta\ \ \text{then}\ \ |f(x) - \ell| \lt \epsilon \end{gather} $$