News for hackers. Stuff that matters.

A comment on The Riemann Hypothesis. Parent comment

Re:The Riemann Hypothesis by Double_Cast on Sunday September 08, 2019 @09:15PM (#20914436)
The problem is that there's different types of multiplication. The fact that multiplication over the Reals can be thought of as "iterated addition" is a consequence of commutativity. But mathematicians often generalize multiplication to various contexts as an arbitrarily-defined transformation, which may or may not be commutative. E.g. multiplication over the Reals is commutative; multiplication over Complex Numbers is commutative; multiplication over Quaternions is non-commutative.

Incidentally, "exponentiation is just repeated multiplication", right? Try using iteration to solve 0^0.

  lim{x -> 0} (0^x) = 0
  lim{x -> 0} (x^0) = 1
The "iteration mindset" doesn't always generalize cleanly.
[ Parent | on HN ]
Re:The Riemann Hypothesis by teekert on Monday September 09, 2019 @02:37AM (#20915711)
It doesn't, but isn't that, in this case, only because you math gals and guys simply define x^0 to be one? There is no logical reason from a geometry standpoint indeed but you needed a definition.
[ Parent | on HN ]
Re:The Riemann Hypothesis by Double_Cast on Monday September 09, 2019 @04:33AM (#20916237)
(x^0) = (1) makes sense because lim{y -> 0} (x^y) = (1).

E.g. (10^0.001) = (1.00230524...)

[ Parent | on HN ]
Re:The Riemann Hypothesis by ukj on Monday September 09, 2019 @03:06AM (#20915866)
On-point.

Exponentiation is not like multiplication because it's not associative.

(2^3)^4 != 2^(3^4)

[ Parent | on HN ]