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
$$f: \mathbb{R} \to \mathbb{R}, f(x) = \left\{\begin{matrix} 42, & \text{falls } x = 0 \\ x, & \text{sonst} \end{matrix}\right.$$
iyadoo la kaashanayo afarta hawlgal xisaabeed ee aasaasiga ah iyadoo la adeegsanayo erey hal saf ah?
Taasi macquul maaha waana ku cadeynaynaa iyadoo la kaashanayo sii socoshada.
Waxaan tixgelinaynaa taxanaha \((x_n)\) wata \(x_n = \frac{1}{n}\) . Taxanahan \( \lim_{ n \to \infty } x_n = \lim_{ n \to \infty } \frac{1}{n} = 0\) . Intaa waxaa sii dheer, \(\lim_{ n \to \infty } f(x_n) = \lim_{ n \to \infty } \frac{1}{n} = 0 \neq 42 = f(0)\) . Marka \(f\) waa la joojiyaa barta \(x=0\) yacni gebi ahaanba waa la joojiyaa.
Sababtoo ah aragtiyaha halabuurka, wadarta iyo wax soo saarka hawlaha joogtada ah ayaa mar kale ah kuwo joogto ah, qofku wuxuu abuuri karaa oo keliya shaqooyin joogto ah (tusaale ahaan, marnaba \(f\) ) iyadoo la adeegsanayo afarta hawlgal 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:
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\(f\) sidoo kale waa la soo bandhigi karaa iyada oo aan jirin haddii / kale qaababka xakamaynta leh:
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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.:
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