General > General Technical Chat
Raising a number to a non-integer power.
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))
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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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