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  1. T

    Bijection, Injection, and Surjection

    So would a bijective homomorphism be an isomorphism? I was taught (working with vector spaces) that a linear bijection is an isomorphism. Are these okay?
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    Infinite sum

    I don't know if this is really adding to the discussion or not, but if you perform the integral test on the (harmonic) series, (using a as any constant, doesn't matter), you end up with \int^{\infty}_{a} dx \frac{1}{x} when integrated gives \ln{x}|^{\infty}_{a} = \ln{\infty} - \ln{a}...
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    Infinite sum

    Yeah weird to think about I guess, but \sum^{\infty}_{i =1} \frac{1}{i} is a divergent series, so it has to be true. Seems that it is not something easy to think about intuitively
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    A shorter proof to 0.999 = 1

    Does anyone have any links to the original discussion from Thanks in advance.
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    What notation would mathematicians use ?

    How would a mathematician write this: \hat{1} = \int dx |x\rangle \langle x| ?