I suspect your knowledge of limits is limited. A function does NOT have to be defined at a point in order for it to have a limit there.Yes, but sinx/x is not defined for x=0. I note that wiki gets squeeze theorem and inequality right (only<), but draws the wrong conclusion, (Lim = 1 by squeeze theorem) the subject of OP.

In fact, if it WAS the case that a function had to be defined at a point in order to have a limit at that point, there would be no such thing as a derivative, since the derivative is defined as $\displaystyle \begin{align*} \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \end{align*}$, even though the function is NOT defined at h = 0.

As another example, consider the limit $\displaystyle \begin{align*} \lim_{x \to 0}\frac{x^2 + x}{x} \end{align*}$. If you drew a graph of the function, you would see that it is identical to $\displaystyle \begin{align*} x + 1 \end{align*}$, except that it has a hole where x = 0. But the function still approaches the same value as you close in on the point x = 0 from both directions. You would most likely have been taught to factorise and cancel, and then substitute the value in. This is fine, in fact it's exactly what you are supposed to do, and you would find that the limiting value is 1. But the function is NOT defined there.

More specifically, the precise definition of a limit is that if you can show for all $\displaystyle \begin{align*} \epsilon > 0 \end{align*}$ that there exists a $\displaystyle \begin{align*} \delta > 0 \end{align*}$ such that $\displaystyle \begin{align*} 0 < \left| x - c \right| < \delta \implies \left| f(x) - L \right| < \epsilon \end{align*}$ then it proves $\displaystyle \begin{align*} \lim_{x \to c} f(x) = L \end{align*}$. Notice the fact that $\displaystyle \begin{align*} 0 < \left| x - c \right| \end{align*}$, this literally means that there has to be some distance between x and c, which means that $\displaystyle \begin{align*} x \neq c \end{align*}$, thereby enabling the function to not need to be defined at $\displaystyle \begin{align*} x = c \end{align*}$ in order for there to be a limit there.