Difference between revisions of "Real numbers"
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(Created page with "The set $\mathbb{R}$ of real numbers is a time scale.") |
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The set $\mathbb{R}$ of real numbers is a [[time scale]]. | The set $\mathbb{R}$ of real numbers is a [[time scale]]. | ||
| + | |||
| + | {| class="wikitable" | ||
| + | |+$\mathbb{T}=\mathbb{R}$ | ||
| + | |- | ||
| + | |Jump operator: | ||
| + | |$\sigma(t)=t$ | ||
| + | |- | ||
| + | |Graininess operator: | ||
| + | |$\mu(t)=0$ | ||
| + | |- | ||
| + | |$\Delta$-derivative: | ||
| + | |$f^{\Delta}(t)=\displaystyle\lim_{h\rightarrow 0} \dfrac{f(t+h)-f(t)}{h}$ | ||
| + | |- | ||
| + | |$\Delta$-integral: | ||
| + | | $\displaystyle\int_s^t f(\tau) \Delta \tau = \displaystyle\int_s^t f(\tau) d\tau$ is the Riemann integral | ||
| + | |} | ||
Revision as of 03:34, 18 May 2014
The set $\mathbb{R}$ of real numbers is a time scale.
| Jump operator: | $\sigma(t)=t$ |
| Graininess operator: | $\mu(t)=0$ |
| $\Delta$-derivative: | $f^{\Delta}(t)=\displaystyle\lim_{h\rightarrow 0} \dfrac{f(t+h)-f(t)}{h}$ |
| $\Delta$-integral: | $\displaystyle\int_s^t f(\tau) \Delta \tau = \displaystyle\int_s^t f(\tau) d\tau$ is the Riemann integral |
