Now, if I recall correctly, in the context of nonstandard analysis, you can technically call the reciprocal of infinity a "differential" (given certain assumptions), but this is avoided in standard analysis (the standard calculus that we use). When talking about infinities, we are typically dealing with limits. read more
The reciprocal of my favourite number, [math]\varsigma=\sqrt{\omega}[/math] (another “infinity” distinct from [math]\omega[/math]), is [math]\frac1{\varsigma}=\sqrt{\epsilon}[/math], an infinitesimal that is infinitely larger than [math]\epsilon[/math] and yet still smaller than any member of [math]\mathbb R[/math], the set of so-called Real numbers. read more