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non-negative_rational_number [2013/05/19 23:27] nikolaj |
non-negative_rational_number [2013/08/12 15:22] nikolaj |
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^ $ \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 47: | Line 39: | ||
Set | Set | ||
=== Subset of === | === Subset of === | ||
- | [[Non-negative real number]] | + | [[Rational number]], [[Non-negative real number]] |
- | === Parents === | + | |
- | [[Natural number]], [[Ordered pair]] | + |