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Is it possible to express a non-negative number/function $\alpha$ mathematically, if we wanted vector: $[\exp(-\alpha|A_1-B|^2),\exp(-\alpha|A_2-B|^2),\exp(-\alpha|A_3-B|^2),...,\exp(-\alpha|A_n-B|^2)]$ to achieve $[0,1,0,...,0]$ where $\exp(-\alpha|A_2-B|^2) \rightarrow 1$ because $|A_2-B|$ is the smallest out of all the squared differences?

Edit: B are all equal

ru111
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  • What would it produce in the event that two terms were equal and the third was larger? – John Hughes Jan 04 '18 at 12:43
  • They would both be 1 – ru111 Jan 04 '18 at 12:49
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    Because $e^{u}$ is never zero, there's no value of $\alpha$ that will do what you ask. You probably need to think about your goals a little longer and express them as clearly as possible in a new question. – John Hughes Jan 04 '18 at 16:06
  • Yes exp(u) is never zero, but I am looking for alpha (if it exists) that allows the limit to 0. The answer may indeed be "there is no such alpha" but I would like to know why in that case. – ru111 Jan 04 '18 at 17:17
  • "allows the limit to be zero": There is no limit in your question. – John Hughes Jan 04 '18 at 23:27

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