Editing Time-scale calculus (section)

=== Operations on time scales===
[[File:Timescales jump operators.png|thumb|upright=2.0|The forward jump, backward jump, and graininess operators on a discrete time scale]]
The ''forward jump'' and ''backward jump'' operators represent the closest point in the time scale on the right and left of a given point <math>t</math>, respectively.  Formally:

:<math>\sigma(t) = \inf\{s \in \mathbb{T} : s>t\}</math> (forward shift/jump operator)
:<math>\rho(t) = \sup\{s \in \mathbb{T} : s<t\}</math> (backward shift/jump operator)

The ''graininess'' <math>\mu</math> is the distance from a point to the closest point on the right and is given by:
:<math>\mu(t) = \sigma(t) -t.</math>

For a right-dense <math>t</math>, <math>\sigma(t)=t</math> and <math>\mu(t)=0</math>.<br />
For a left-dense <math>t</math>, <math>\rho(t)=t.</math>