Hoʻohana ʻia nā pale curly i ka notation o ka wehewehe ʻana i ka hana me ka ʻokoʻa o ka hihia. Alualu mākou i ka nīnau maʻalahi inā hiki ke hoʻopau ʻia kēia hōʻike a hiki ke hoʻoliʻiliʻi i ka hana i kahi notation me ka ʻole o ia. ʻO kahi laʻana, ka hana
$$f: \mathbb{R} \to \mathbb{R}, f(x) = \left\{\begin{matrix} 42, & \text{falls } x = 0 \\ x, & \text{sonst} \end{matrix}\right.$$
hōʻike iā ia ma ka huaʻōlelo hoʻokahi laina me ka hoʻohana ʻana i nā hana helu kumu ʻehā?
ʻAʻole hiki kēlā a hōʻoia mākou me ke kōkua o ka hoʻomau.
Manaʻo mākou i ke kaʻina \((x_n)\) me \(x_n = \frac{1}{n}\) . No kēia kaʻina \( \lim_{ n \to \infty } x_n = \lim_{ n \to \infty } \frac{1}{n} = 0\) . Eia kekahi \(\lim_{ n \to \infty } f(x_n) = \lim_{ n \to \infty } \frac{1}{n} = 0 \neq 42 = f(0)\) . 'O ia ho'i, 'o \(f\) ka 'oki 'ana ma ke kiko \(x=0\) , a no laila 'o ka pau 'ana o ka holo'oko'a.
Ma muli o ka hoʻomau hou ʻana o ka huina a me ka huahana o nā hana hoʻomau ma muli o ka concatenation theorems, hiki iā ʻoe ke hana i nā hana hoʻomau (ʻoiai ʻaʻole loa \(f\) ) me ka hoʻohana ʻana i nā hana helu kumu ʻehā.
Eia nō naʻe, inā ʻae mākou i ka hana signum discontinuous, no ka laʻana, hiki iā mākou ke loaʻa maʻalahi kahi ʻano inoa. A laila ʻo ia hoʻi
$$f: \mathbb{R} \to \mathbb{R}, f(x) = sgn^2(x-42)+42.$$
No kahi hana maʻamau \(f\) me ka hoʻokaʻawale ʻana i ka hihia
$$f,g,h,a: \mathbb{R} \to \mathbb{R}, f(x) = \begin{Bmatrix} g(x), & \text{falls } a(x) = 0 \\ h(x), & \text{falls } a(x) \neq 0 \end{Bmatrix} = sgn^2 \left(a(x)\right)\cdot h(x) + \left(1-sgn^2\left(a(x)\right)\right)\cdot g(x).$$
Ma ka ʻaoʻao ʻē aʻe, inā ʻoe e nānā i nā hana i nā ʻōlelo papahana, hiki ke hoʻoholo ʻia nā lālā. ʻO kahi laʻana, ma PHP hiki ke palapala ʻia ka hana signum me:
e367d0ca10c4f0ac43640ad7fd1b3f0d
\(f\) hiki ke hōʻike pū ʻia me ka ʻole inā / ʻē aʻe ka mālama ʻana i nā hale me:
e367d0ca10c4f0ac43640ad7fd1b3f0d
Inā makemake ʻoe e hana me ka ʻole o nā mea hoʻohālikelike, hiki iā ʻoe ke hele i kahi ʻanuʻu hou aʻe a luʻu i loko o ka honua kupaianaha o nā mea hoʻohana bitwise.:
e367d0ca10c4f0ac43640ad7fd1b3f0d