There is a limit point for a bounded infinite set. This statement is
1. Cauchy’s Mean Value Theorem
2. Taylor’s Theorem
3. Darboux’s Theorem
4. Bolzano Weierstrass Theorem
1. Cauchy’s Mean Value Theorem
2. Taylor’s Theorem
3. Darboux’s Theorem
4. Bolzano Weierstrass Theorem
Correct Answer – Option 4 : Bolzano Weierstrass Theorem
Bolzano Weierstrass Theorem:
The theorem says that there is a limit point for a bounded infinite set S.
Let Ø ≠ S ⊆ R and S be bounded and infinite. Then there exists a limit point of S (in R ).
Another Statement– Every sequence has a monotone subsequence.