This video explains the Boundedness Theorem in the most simple and easy way possible, whose statement is, Let, I=[a,b] be a closed bounded interval and let f:I→R be continuous on I. Then, f is bounded on I.

CORRECTION: At 2:11 and 6:14 both "n" and "r" belong to the set of Natural Numbers instead of set of Real Numbers.
REASON: Both "n" and "r" represent the elements of the sequence f(x_n) which are basically f(x_1), f(x_2), f(x_3), ... , f(x_n) and for instance they can't be f(x_0.1), f(x_7.89) etc.

Every convergent sequence is bounded Proof:
   • Every convergent sequence is bounded ...  

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