exponentiation - Prove that $i^i$ is a real number - Mathematics …
Over the reals, the concept that "exponentiation = repeated multiplication" breaks down when you have non-integer exponents, so you have to start defining exponentiation using suprema of sets, which exploits the ordered field nature of the reals. The complex field is not an ordered field, so the equivalent notion of a supremum doesn't exist.
exponentiation - What's the inverse operation of exponents ...
Oct 3, 2014 · You know, like addition is the inverse operation of subtraction, vice versa, multiplication is the inverse of division, vice versa , square is the inverse of square root, vice versa. What's the in...
What is the exponent of a group? - Mathematics Stack Exchange
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exponentiation - How does an exponent work when it's less than …
Oct 7, 2016 · That is why a lot of definitions need to be justified by theorems. In this case we extend the old structure (reals with integer exponentiation) to a new one (reals with rational exponentiation), and have to prove that the new structure …
Meaning of a set in the exponent - Mathematics Stack Exchange
Thanks for pointing this out, Asaf. To avoid any anomalies, you may indeed want to distinguish set exponentiation from, say, exponentiation on the natural numbers when it is defined only as repeated multiplication. $\endgroup$ –
exponentiation - order of operations with many level exponents ...
Feb 3, 2015 · exponentiation. Linked. 2. A basic power problem. Related. 2. Why are exponents not associative? 0 ...
exponentiation - Calculating Irrational and Fractional Powers of a ...
Oct 3, 2024 · If you are skilled in written computation, you can form a table of successive square roots, starting from $3$ (i.e. exponents $\frac12,\frac14,\frac18\cdots$).
exponentiation - How to calculate a decimal power of a number ...
$\begingroup$ I disagree, you can actually write any decimal as a fraction. 0.14 is fourteen hundredths, or simplified 7/50. then add in 2/1 by raising to lowest common denominator, you end up with 2.14=107/50.
exponentiation - Exponential Equation with base -1, 0, and 1 ...
Oct 12, 2017 · we will call this an exponentiation function because its formula consists of an exponentiation. But this is a problem of language and the human mind that he will use such a word in this situation. In the sense of your book's definition this is not an exponentiation function, even if it is a function.
exponentiation - Comparing large exponents - Mathematics Stack …
Jul 10, 2015 · exponentiation; Share. Cite. Follow edited Jul 10, 2015 at 14:27. Sloan. 2,354 1 1 gold badge 12 12 silver ...