| General > General Technical Chat |
| Raising a number to a non-integer power. |
| << < (4/13) > >> |
| 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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