Matematika je jezik

Kaj je interval?

Vzemimo realni števili a in b tako, da je a < b.

Vse točke med a in b predstavljajo množico realni števil in to množico imenujemo interval.

interval

 

 

 

 

Števili a in b sta krajišči intervala.

Zaprti interval vključuje poleg vseh števil med a in b tudi obe krajišči. Oznaka za zapri interval je [ ali ].

Odprti interval pa ne vsebuje krajišč. Oznaka za odpri interval je ( ali ).

PRIMERI:

ZAPRTI INTERVAL

[a, b] = {x \in \!\, \mathbb{R} \!\, ; a \le \!\, x \le \!\, b} 

zaprti interval

 

 

 

 

ODPRTI INTERVAL

(a, b) = {x \in \!\, \mathbb{R} \!\, ; a < x < b} 

odprti interval

 

 

 

 

NA LEVO ODPRTI IN NA DESNO ZAPRTI INTERVAL

(a, b] = {x \in \!\, \mathbb{R} \!\, ; a < x \le \!\, b} 

na levo odprti interval in na desno zaprti interval

 

 

 

 

NA DESNO ODPRTI IN NA LEVO ZAPRTI INTERVAL

[a, b) = {x \in \!\, \mathbb{R} \!\, ; a \le \!\, x < b} 

na desno odprti interval in na levo zaprti interval

 

 

 

 

Oglati oklepaj označuje, da krajišče sodi k intervalu, okrogli oklepaj pa, da krajišče ne sodi k intervalu.

 


POMEMBNO ZA RAZUMEVANJE:

Kaj so realna števila?

Realna števila na številski premici

Množice in računanje z množicami


Določanje intervala 1 »

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