The Bolzano–Weierstrass theorem is named after mathematicians Bernard Bolzano and Karl Weierstrass. It was actually first proved by Bolzano in 1817 as a lemma in the proof of the intermediate value theorem. Some fifty years later the result was identified as significant in its own right, and proved again by Weierstrass. It has since become an essential theorem of analysis.
the bolzano–wEierstRasS theorem Is named aftEr mathEmaticiaNs bernArd BOLzano anD Karl wEiersTraSS. it WAs actuaLLy fiRst proveD By bOLzano IN 1817 as a LemMa in thE prOOf Of the iNteRMEDiAte value tHeorEm. soME FiftY yearS LaTeR tHE ResuLt wAs IdeNtIfIed As significaNt in its oWn rIGht, and pROved aGaiN bY wEiersTrass. iT hAs siNcE becOME an EsSEntIal ThEorEm of AnAlYSiS.