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Math Help - Infinite Dimensional Vector Space

  1. #1
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    Infinite Dimensional Vector Space

    Dear Members
    Kindly guide me about Infinite Dimensional Vector Space? I am requested to give easy examples Infinite Dimensional Vector Space with proof.
    Waiting for good response.
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  2. #2
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    Re: Infinite Dimensional Vector Space

    The space of polynomials over an infinite field (where the vectors are the coefficients of each power of x).
    \{0,1\}^\infty (each coordinate is either zero or one, and the addition is 0+0=1+1=0, 0+1=1+0=1). Over the field \Bbb{F}_2.
    \Bbb{R}^\infty
    The space of continuous functions f:\Bbb{R}\to \Bbb{R}
    \mathcal{L}^p spaces
    The list goes on...

    What sort of examples are you looking for. Try looking up Infinite Dimensional Vector Space examples.
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  3. #3
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    Re: Infinite Dimensional Vector Space

    Dear SlipEternal
    Thanks for your kind guidance.
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