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]].
 +
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{| class="wikitable"
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|+$\mathbb{T}=\mathbb{R}$
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|-
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|Jump operator:
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|$\sigma(t)=t$
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|-
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|Graininess operator:
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|$\mu(t)=0$
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|-
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|$\Delta$-derivative:
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|$f^{\Delta}(t)=\displaystyle\lim_{h\rightarrow 0} \dfrac{f(t+h)-f(t)}{h}$
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|-
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|$\Delta$-integral:
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| $\displaystyle\int_s^t f(\tau) \Delta \tau = \displaystyle\int_s^t f(\tau) d\tau$ is the Riemann integral
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|}

Revision as of 03:34, 18 May 2014

The set $\mathbb{R}$ of real numbers is a time scale.

$\mathbb{T}=\mathbb{R}$
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