# Notation for delaying choice between strict and weak inequality

Is there an established notation for representing a choice between $$<$$ and $$\le$$ ?

I like delaying the choice between committing to a weak inequality or a strict inequality for as long as possible, in situations where it's possible to delay making a commitment.

For instance, consider the $$\varepsilon$$-$$\delta$$ definition of continuity at a point (100).

$$f \mathop{\text{continuous at}} x \stackrel{\text{def}}{\iff} \forall \varepsilon > 0 \mathop. \exists \delta \mathop. \forall s \mathop. |x-s| < \delta \to |f(s)-f(x)|<\varepsilon \tag{100}$$

I am not certain whether "$$\forall \varepsilon > 0$$" can be replaced with "$$\forall \varepsilon \ge 0$$" , but the remaining $$\lt$$ symbols can definitely be replaced without changing the extension of the definition.

Is there an established way to mark a choice between, say, $$<$$ and $$\le$$ and some good rules of thumb for avoiding problems?

For instance, the $$\pm$$ symbol is useful in circumstances like the following for compactly representing some kind of choice between $$\lambda x \mathop. - x$$ and $$\lambda x \mathop. x$$.

$$\sqrt{-1} = \pm i \tag{101}$$

Or

$$|x| = 4 \implies x = \pm 4 \tag{102}$$

In (102), $$\pm$$ clearly has some kind of disjunctive meaning. I'm not sure how to interpret $$\pm$$ in (101), but it seems clear in practice.