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non-negative_rational_number [2013/05/19 23:16] nikolaj |
non-negative_rational_number [2013/08/12 15:11] nikolaj |
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| ==== Ramifications ==== | ==== Ramifications ==== | ||
| - | |||
| - | === Satisfies === | ||
| - | |||
| - | $ \mathbb N\subset \mathbb Q_+ $ | ||
| === Definitions === | === Definitions === | ||
| Line 23: | Line 19: | ||
| ^ $ \mathrm{red}(a,b):=a\div\mathrm{gcd}(a,b)$ | | ^ $ \mathrm{red}(a,b):=a\div\mathrm{gcd}(a,b)$ | | ||
| - | ^ $ \frac{a}{b} \equiv $ | | + | ^ $ \frac{a}{b} \equiv \begin{cases} \mathrm{red}(a,b) & \mathrm{if}\ \mathrm{red}(b,a)=1\\\\ \langle\mathrm{red}(a,b),\mathrm{red}(b,a)\rangle & \mathrm{else} \end{cases}$ ^ |
| - | + | ||
| - | \begin{cases} | + | |
| - | + | ||
| - | \mathrm{red}(a,b)\hspace{1cm}\mathrm{if}\ \mathrm{red}(b,a)=1 | + | |
| - | + | ||
| - | \langle\mathrm{red}(a,b),\mathrm{red}(b,a)\rangle\hspace{1cm}\mathrm{else} | + | |
| - | + | ||
| - | \end{cases} | + | |
| ^ $ \mathrm{num}\frac{a}{b}\equiv a $ ^ | ^ $ \mathrm{num}\frac{a}{b}\equiv a $ ^ | ||
| Line 52: | Line 40: | ||
| === Subset of === | === Subset of === | ||
| [[Non-negative real number]] | [[Non-negative real number]] | ||
| - | === Parents === | ||
| - | [[Natural number]], [[Ordered pair]] | ||
