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 $\lambda x \mathop. x$.

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


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

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.


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