General > General Technical Chat

Raising a number to a non-integer power.

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Alex Eisenhut:
For that matter, how can you multiply a number by itself a negative number of times?

RoGeorge:

--- Quote from: TimFox on May 27, 2020, 07:11:36 pm ---(I can't find lower-case omega here)
--- End quote ---

EEVblog forum can render LaTex notation.  Lower case Omega can be written as

--- Code: ---\$\omega\$

--- End code ---
That will be displayed as \$\omega\$.

daqq:

--- Quote from: T3sl4co1l on May 27, 2020, 03:17:43 pm ---
--- Quote from: mark03 on May 27, 2020, 03:12:31 pm ---What is this number i that you speak of?

--- End quote ---

You must be 'j'oking ;D

Tim

--- End quote ---
He probably just imagined it.

Kleinstein:

--- Quote from: Alex Eisenhut on May 27, 2020, 07:18:20 pm ---For that matter, how can you multiply a number by itself a negative number of times?

--- End quote ---

This one is easy:  the negative exponents give the inverse. So  A^(-B)  =  1 / A^B.
So multiply -2 times is the same as dividing 2 times.

magic:

--- Quote from: Kleinstein on May 27, 2020, 09:43:56 am ---One can use the logarithm and exponential to rewrite the power:
 A^B =  exp( B * ln(A))

--- End quote ---
Yeah, I guess you can do that, but then you need to define exp(x) as something other than ex to avoid circular definition.

It can be done, there are weird-ass formulas which resolve to ex without explicitly mentioning e itself and taking powers of it.
But actually teaching it that way is an exercise in applied obfuscation.


--- Quote from: TimFox on May 27, 2020, 07:14:17 pm ---I also learned that the formal definition of exponentiation in modern mathematics is the one involving logarithms, which is required when the exponent is not a rational fraction.

--- End quote ---
Not required. I have defined it without a single stinkin' logarithm ;)

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