# Limits of Functions Notation

As I'm working on my "derivatives of polynomial functions," and I'm learning about limits. This as goes well, except for the notation part. The first notation I encounter is
$$\lim_{x \to a} f(x)$$ My textbook says I should read this as "limit for $x$ nearing $a$" or "limit in $a$." I am however not given any explanation as to why this is so, and how to adapt my reading to other formulas. So when I stumbled upon the next one...
$$\lim_{h \to 0} 0=0$$ ...I had no idea what this stood for. I'm guessing "the limit of $0$ with $h$ nearing $0$ is zero." But even if that's so, I've got no idea as to which zero stands for what and why. A bit of background info is that this last notation was the result of an example about derivatives with $y = 3$. The coordinates of the first point were $(1,3)$ and those of the second were $(1+h,3)$. The difference quotient was $0$.

If you could please explain how to read this notation and others of the like, and which part of the notation means what exactly (so that I can read others and know how to change my reading), that would be of great help!

• $0$ stands for $0.$ Suppose $f(h)=0$ for every $h$. Then $\lim_{h\to 0}f(h)=f(0)=0$. But every $f(h)$ IS 0 so we can replace $f(h)$ with $0$ wherever $f(h)$ appears – DanielWainfleet Apr 17 '18 at 21:56
The notation $$\lim_{x\to a}f(x)$$ is read as 'limit of the function $f(x)$ as $x$ approaches/moves near to/ tends to the number $a$.'
The $\lim$ is just shorthand for limit; $f(x)$ I hope you know; and the symbol $x\to a$ tells you that the variable $x$ gets closer and closer to the value $a$ (and sometimes $a$ can stand for $\pm\infty$). As time goes by you will get used to it, and maybe even get to see how it is a most natural notation for expressing a limit.