So I've always thought that "$\Delta$" when applied to an n-tuple or scalar was the change of that n-tuple or scalar relative to a previous state in time and proportional to the amount of time or $\Delta \bf{x}=\frac{\bf{x_u}-\bf{x_i}}{t_u-t_i}$ so I always wrote the acceleration of a mass as $\Delta^2 M_p$ but now I am unsure whether this is in fact correct. My question is: What are all of the different ways Delta can be used as well as am I using it correctly?
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