undefined | Better HN

0 pointsPeaker14y ago0 comments

That explanation is somewhat problematic with fractional exponents.

The generalization of exponentiation makes the "multiply N times" explanation fail.

0 comments

2 comments · 1 top-level

nitrogen14y ago· 1 in thread

Not really; a fractional exponent n yields the quantity one would have to multiply 1/n times to return the original value. Multiplication an integer number of times could be seen as a special case of a broader concept of "fractional" multiplication (much like the gamma function (Γ(n)) extends the discrete factorial to a continuous domain).

PeakerOP14y ago

1/n times may not necessarily be whole either.

How do you explain irrational exponents this way, for example? What about complex exponents?

Indeed you can extend the special case to the continuous domain -- but then the definition is expanded as well.

I still think "multiply N times" is just a special-case, and as such, not usable as a definition -- let alone an explanation of why we can add exponents in the general case.

j / k navigate · click thread line to collapse