Qaybaha qalooca waxaa loo isticmaalaa qoraalo qeexitaan shaqeed oo leh kala duwanaansho kiis. Waxaan dabagal ku sameynaa su'aasha fudud ee ah in matalaadan sidoo kale la baabi'in karo oo howsha loo yareyn karo ogeysiis sameyn karta la'aantood. Tusaale ahaan, shaqada
$$f: \mathbb{R} \to \mathbb{R}, f(x) = \left\{\begin{matrix} 42, & \text{falls } x = 0 \\ x, & \text{sonst} \end{matrix}\right.$$
ma uga dhigan tahay hal-line erey adoo isticmaalaya afarta hawlood ee aasaasiga ah ee xisaabta?
Taasi macquul maaha waana ku cadeynaynaa iyadoo la kaashanayo sii socoshada.
Waxaan tixgelineynaa taxanaha \((x_n)\) ee leh \(x_n = \frac{1}{n}\) . Taxanahan \( \lim_{ n \to \infty } x_n = \lim_{ n \to \infty } \frac{1}{n} = 0\) . Intaa waxaa dheer \(\lim_{ n \to \infty } f(x_n) = \lim_{ n \to \infty } \frac{1}{n} = 0 \neq 42 = f(0)\) . Tani waxay ka dhigan tahay in \(f\) uu joogsanayo barta \(x=0\) , sidaas darteedna la joojiyo guud ahaan.
Maadaama wadarta iyo wax soo saarka hawlaha joogtada ahi ay yihiin kuwo joogto ah mar kale iyadoo ay ugu wacan tahay aragtiyaha isku xidhka, kaliya waxaad dhalin kartaa hawlo joogto ah (gaar ahaan waligaa \(f\) ) adoo isticmaalaya afarta hawlood ee xisaabinta aasaasiga ah.
Si kastaba ha noqotee, haddii aan u oggolaano shaqada calaamadaha joojinta, tusaale ahaan, waxaan si fudud u heli karnaa ogeysiis noocaas ah. Kadibna waa
$$f: \mathbb{R} \to \mathbb{R}, f(x) = sgn^2(x-42)+42.$$
Shaqada guud \(f\) leh kala duwanaansho kiis ayaa lagu dabaqayaa
$$f,g,h,a: \mathbb{R} \to \mathbb{R}, f(x) = \begin{Bmatrix} g(x), & \text{falls } a(x) = 0 \\ h(x), & \text{falls } a(x) \neq 0 \end{Bmatrix} = sgn^2 \left(a(x)\right)\cdot h(x) + \left(1-sgn^2\left(a(x)\right)\right)\cdot g(x).$$
Dhinaca kale, haddii aad eegto howlaha ku jira luuqadaha barnaamijka, laamaha waa la xallin karaa. Tusaale ahaan, PHP shaqada calaamadeynta waa lagu tashan karaa:
e367d0ca10c4f0ac43640ad7fd1b3f0d
\(f\) sidoo kale waa la soo bandhigi karaa iyada oo aan jirin haddii / kale qaababka xakamaynta leh:
e367d0ca10c4f0ac43640ad7fd1b3f0d
Haddii aad sidoo kale rabto inaad sameyso iyada oo aan lahayn hawl wadeennada isbarbardhigga, waxaad tallaabo dheeraad ah u gudbi kartaa oo aad u dhex geli kartaa adduunka cajiibka ah ee hawl wadeennada bitwise.:
e367d0ca10c4f0ac43640ad7fd1b3f0d