# Ukuhamba notation ngemisebenzi enamasebe0820

Iibakaki ezisongekileyo zisetyenziselwa ukubhalwa kweenkcazo zomsebenzi ngokwahlulahlula amatyala. Silandela umbuzo olula wokuba lo mmeli ungasuswa na kwaye umsebenzi ungancitshiswa ube ngumbhalo onokuwenza ngaphandle kwawo. Umzekelo, umsebenzi

$$f: \mathbb{R} \to \mathbb{R}, f(x) = \left\{\begin{matrix} 42, & \text{falls } x = 0 \\ x, & \text{sonst} \end{matrix}\right.$$

ngoncedo lweendlela ezine ezisisiseko zezibalo usebenzisa igama lomgca omnye?

Ayinakwenzeka loo nto kwaye siyakungqina oko ngoncedo lokuqhubekeka.

Sijonga ulandelelwano $$(x_n)$$ nge $$x_n = \frac{1}{n}$$ . Kolu landelelwano $$\lim_{ n \to \infty } x_n = \lim_{ n \to \infty } \frac{1}{n} = 0$$ . Ukongeza, $$\lim_{ n \to \infty } f(x_n) = \lim_{ n \to \infty } \frac{1}{n} = 0 \neq 42 = f(0)$$ . Ke $$f$$ ayipheleli kwinqanaba $$x=0$$ okt iyapheliswa iyonke.

Kuba isixa kunye nemveliso yemisebenzi eqhubekayo iyaqhubeka kwakhona ngenxa yamagatya okudityaniswa, umntu unokuvelisa kuphela imisebenzi eqhubekayo ngoncedo lwemisebenzi emine esisiseko ye-arithmetic (ngakumbi soze $$f$$ ).

Nangona kunjalo, ukuba sivumela umsebenzi ophelileyo wokungena, umzekelo, sinokulufumana ngokulula ulwaziso olunjalo. Ke oko kukuthi

$$f: \mathbb{R} \to \mathbb{R}, f(x) = sgn^2(x-42)+42.$$

Umsebenzi ngokubanzi $$f$$ ngokwahlulahlula iimeko kuyasebenza

$$f,g,h,a: \mathbb{R} \to \mathbb{R}, f(x) = \begin{Bmatrix} g(x), & \text{falls } a(x) = 0 \\ h(x), & \text{falls } a(x) \neq 0 \end{Bmatrix} = sgn^2 \left(a(x)\right)\cdot h(x) + \left(1-sgn^2\left(a(x)\right)\right)\cdot g(x).$$

Kwelinye icala, ukuba ujonga imisebenzi kwiilwimi zenkqubo, amasebe anokusonjululwa. Umzekelo, kwi-PHP umsebenzi wesayina ungaphawulwa ngemephu:

$$f$$ inokuboniswa ngaphandle kwayo nayiphi na enye into / ezinye izakhiwo zolawulo nge: