es, men Bolzano-Weierstrass teoremasining oddiy isbotini taqdim eta olaman: Bolzano-Weierstrass teoremasi shuni ko'rsatadiki, $\mathbb{R}$ dagi har bir chegarali ketma-ketlikning konvergent kichik ketma-ketligi bor. Isbot: ${a_n) $ $\mathbb{R}$ dagi chegarali ketma-ketlik bo'lsin. Ya'ni, $m,M \mathbb{R}$ mavjud bo'lishi mumkin, shunda $m \leq a_n \leq M$ barcha $n \mathbb{N}$ uchun. $[m,M]$ intervalini ikkita kichik qiymatga bo'ling: $[m,\frac{m+{M2}$] va $[\frac{m+{M2}$,
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