Ib "tsawg kawg sab sauv" rau ib txheej ces ib sab qaum uas me npaum li sai tauQhov ntawd yog, nws yog ib sab qaum uas me dua li lwm sab sauv khi. Cov ciam teb loj tshaj plaws yog txhais zoo ib yam. Definition: Cia ua ib tug subset uas yog bounded saum toj no.
Tus piv txwv saum toj kawg nkaus yog dab tsi?
Txhua tus lej uas ntau dua lossis sib npaug rau tag nrho cov ntsiab lus ntawm lub teeb. Qhov tsawg tshaj plaws ntawm tag nrho cov ciam teb sab sauv ntawm ib pawg ntawm cov lej. Piv txwv li, qhov tsawg kawg nkaus sab sauv ntawm lub caij nyoog (5, 7) yog 7.
Yuav ua li cas koj pom qhov tsawg kawg nkaus?
Definition 6 A yam tsawg kawg sab sauv los yog supremum rau A yog ib tug number u ∈ Q hauv R xws li (i) u yog ib sab qaum rau A; thiab (ii) yog U yog lwm sab qaum rau A ces U ≥ u. Yog hais tias muaj ib tug supremum, nws yog denoted los ntawm supA. Piv txwv 7 Yog tias A=[0, 1] ces 1 yog qhov tsawg kawg sab sauv rau A.
Dab tsi yog qhov tsawg kawg sab sauv ntawm txoj haujlwm?
Nyob rau hauv tag nrho cov piv txwv hais saum toj no, qhov tsawg kawg nkaus sab sauv rau f(x) yog qhov siab tshaj plaws ntawm f(x) Qhov no yog ib txwm yog f(x) muaj qhov siab tshaj plaws. Ib yam li ntawd, qhov loj tshaj plaws hauv qab yog qhov tsawg kawg nkaus ntawm f(x) yog f(x) muaj qhov tsawg kawg nkaus. ib=n − n n + 1=0 uas qhia peb tias yog qhov txwv muaj, nws yuav tsum yog 0.
Yuav ua li cas koj thiaj paub tias ib yam dab tsi yog sab sauv lossis qis?
Yog tias koj faib ib qho kev ua haujlwm polynomial f(x) los ntawm (x - c), qhov twg c > 0, siv hluavtaws faib thiab qhov no ua rau tag nrho cov lej zoo, ces c yog qhov txuas sab saud rau cov hauv paus hauv paus ntawm qhov sib npaug. f(x)=0 Nco ntsoov tias ob yam yuav tsum tshwm sim rau c kom ua rau sab sauv. Ib qho yog c > 0 lossis zoo.
