# Time

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Related KMR-pages:

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Other relevant sources of information:

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How many ticks does it take
to take it back
to where it started?

Different types of clocks: $\, 7 \, , \{ 12, 2 \} \, , 24 \, , { \{ 28, 29, 30, 31 \} }^{12} \, , {\{ 365, 366 \}}^{ \, n \; ≥ \; 1583 } \,$

hours, days, weeks, months, years, decades, centuries, millennia, …

Expanding the duration of each tick:

$\, N_{days} \, = \, 7 \times N_{weeks} \,$

$\, N_{hours} \, = \, 24 \times N_{days} \,$

$\, N_{years} \, = \, 10 \times N_{decades} \,$

$\, N_{decades} \, = \, 10 \times N_{centuries} \,$

$\, N_{centuries} \, = \, 10 \times N_{millennia} \,$

Modular arithmetic: $\;\; x \, + \, n \times a \, \equiv \, x \pmod n \, \equiv \, x \pmod a \, , \forall \, x, n, a \in \mathrm Z.$

What this formula means (in plain English) is that the integers $\, x \,$ and $\, x + n \times a \,$
have the same remainder when you divide them by either the integer $\, a \,$ or the integer $\, n$.

• Arithmetical crossfire

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Weekday calendar:

$\, N_{days} \, = \, 7 \times N_{weeks} \,$

$\, \mathbb{Z} \, / \, 7\mathbb{Z} \, = \, {\mathbb{Z}}_7 \,$

Question: What is the weekday a million days from now?

$\, {10}^6 \pmod 7 \, \equiv \, 1 \, \in \, {\mathbb{Z}}_7$.

Answer: The same weekday as tomorrow.

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The shifting sequence of moments:

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