The hypotheses and thesis of both the Bolzano and Weierstrass theorems are analysed in detail with relation to continuous functions.

Some of the most significant applications of these theorems are focused on.

• To understand the significance of the concepts hypothesis and thesis as part of a mathematical theorem.

• To learn two basic theorems related to continuous functions.

• To use some basic concepts of Analysis such as continuity and endpoints.

• To see some important applications of the theorems.