Science Memes

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omg (lemmy.dbzer0.com)

submitted 1 week ago by [email protected] to c/[email protected]

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[–] [email protected] 29 points 1 week ago* (last edited 1 week ago) (1 children)

Observe the identities

a / b = a × b^(-1)   (A)

sqrt(a) = a ^ (1/2)  (B)

a^b × a^c = a^(b+c)  (C)

(a^b)^c = a^(b × c)  (D)

and derive

  2 / sqrt(2)
= 2 / 2^(1/2)           (B)
= 2 × [2^(1/2)] ^ (-1)  (A)
= 2 × 2^(1/2 × (-1))    (D)
= 2 × 2^(-1/2)
= 2 ^ [1 + (-1 / 2)]    (C)
= 2 ^ (1/2)
= sqrt(2)               (B)

[–] [email protected] 7 points 1 week ago (1 children)

Neat breakdown! Can you explain why this line =2^(1+ -1/2) =>2^(-1/2) shouldn’t it be 2^(1/2) or am I missing something? Second guessing myself here lol

[–] [email protected] 14 points 1 week ago (1 children)

No, that’s a mistake. Incredible how many mistakes one can make in a simple derivation.

Thanks for pointing it out.

[–] [email protected] 3 points 1 week ago

All good! Thanks for the very helpful explanation.