Explore BrainMass

Explore BrainMass

    Space of continuous functions

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Let C[0,1] be the space of continuous real functions where C[0,1] has the following norm
    ||f||_2 =( integral (from 0 to 1) |f(t)|dt)^(1/2)

    Consider f_n(t) = 0
    for t greater than or equal to zero and less than or equal to 1/2-1/n,
    f_n(t)=1+n(t-1/2) for t great than or equal to 1/2-1/n and t less than or equal to 1/2
    and f_n(t)=1 when t is greater than or equal to 1/2 and t less than or equal to 1

    Prove that {f_n} is a Cauchy sequence in (C[0,1], ||,||)

    © BrainMass Inc. brainmass.com December 24, 2021, 9:16 pm ad1c9bdddf
    https://brainmass.com/math/integrals/modelling-the-space-of-continuous-functions-361061

    SOLUTION This solution is FREE courtesy of BrainMass!

    Please see the attachment.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 9:16 pm ad1c9bdddf>
    https://brainmass.com/math/integrals/modelling-the-space-of-continuous-functions-361061

    Attachments

    ADVERTISEMENT