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  • apolo399@lemmy.worldtoScience Memes@mander.xyz1 + 1
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    4 months ago

    No, it’s correct. You define the operation by it’s properties. It’s not saying that “a plus 0 = a” but “the result of applying the binary operation ‘+’ to any number with 0 should give the original number.”

    • is just a symbol. You could instead write it as +(a,0)=a and +(a,S(b))=S(+(a,b)).

    You have to have previously defined 1=S(0), 2=S(1), 3=S(2), and so on.





  • apolo399@lemmy.worldtoScience Memes@mander.xyzI just cited myself.
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    5 months ago

    Sure, let’s do it in base 3. 3 in base 3 is 10, and 3^(-1) is 10^(-1), so:

    1/3 in base 10 = 1/10 in base 3
    0.3… in base 10 = 0.1 in base 3

    Multiply by 3 on both sides:

    3 × 0.3… in base 10 = 10 × 0.1 in base 3
    0.9… in base 10 = 1 in base 3.

    But 1 in base 3 is also 1 in base 10, so:

    0.9… in base 10 = 1 in base 10