# Big Oh notation help?

Can someone please explain what it means to say something like
$$x = x_0 + \mathcal{O}(y)$$
?

arildno
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Nothing.

You must include in your expression a "as x goes to.."

Without that, it is meaningless.

$\cos x = 1 + O(x^2)$ as $x \to 0$ means:
$$\frac{\cos x - 1}{x^2}$$
is bounded in some neighborhood of $0$ .