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My previous/alt account is yetAnotherUser@feddit.de which will be abandoned soon.

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  • yetAnotherUser@discuss.tchncs.detoScience Memes@mander.xyzWitchcraft
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    23 days ago

    But the first few values are:

    1 + 1/3 + 1/6 + 1/10 + 1/15 + 1/21 + 1/28…

    I really don’t see any pattern there showing why it converges to 2 exactly

    Edit:

    After thinking some more, you could write the sum as:

    (Sum from n=1 to infinity of): 2/(n * (n + 1))

    That sum is smaller than the sum of:

    2 * (1/n2) which converges to π2/3

    So I can see why it converges, just not where to.



  • Well, as much as possible anyway. When considering mass alone, life is quite efficient.

    According to Wolfram Alpha:

    The sun produces 3.8 * 1028 watts.

    A single human produces 104 watts (calculated through the average caloric intake assuming that intake ≈ energy consumption) through heat radiation.

    Therefore:

    1 kg of human converts 1.5 watt into heat.

    1 kg of the sun converts 0.0002 watt into (heat) radiation.

    And while I have nearly no understanding how entropy is calculated, from those values alone it seems like humans produce more entropy per kg than the sun. I’m pretty sure entropy is somewhat related to energy production though.






  • Yes, but similar flaws exist for your proof.

    The algebraic proof that 0.999… = 1 must first prove why you can assign 0.999… to x.

    My “proof” abuses algebraic notation like this - you cannot assign infinity to a variable. After that, regular algebraic rules become meaningless.

    The proper proof would use the definition that the value of a limit approaching another value is exactly that value. For any epsilon > 0, 0.999… will be within the epsilon environment of 1 (= the interval 1 ± epsilon), therefore 0.999… is 1.


  • yetAnotherUser@discuss.tchncs.detoScience Memes@mander.xyzI just cited myself.
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    3 months ago

    Unfortunately not an ideal proof.

    It makes certain assumptions:

    1. That a number 0.999… exists and is well-defined
    2. That multiplication and subtraction for this number work as expected

    Similarly, I could prove that the number which consists of infinite 9’s to the left of the decimal separator is equal to -1:

    ...999.0 = x
    ...990.0 = 10x
    
    Calculate x - 10x:
    
    x - 10x = ...999.0 - ...990.0
    -9x = 9
    x = -1
    

    And while this is true for 10-adic numbers, it is certainly not true for the real numbers.