2014年3月8日 · Exponentiation is a correspondence between addition and multiplication. Think of a number line, with $0$ in the "middle", and tick marks at each integer. Moving a certain distance to the right corresponds to adding a positive number, and adding the same number moves you the same distance, no matter where you are on the line.

2014年10月3日 · 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...

2015年11月20日 · There can't be just one word denoting the result of applying exponentiation to a pair of numbers. For example, if I gave ou the problem of applying the exponentiation operation to the pair of numbers $2$ and $3$ and that was all the information I provided you, you'd have no way of knowing whether I meant $2^3=8$ or $3^2=9$.

2012年9月5日 · 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.

$\begingroup$ 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.

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2017年11月3日 · Rather than trying to press complex exponentiation into the mold of repeated multiplication, see complex exponentiation -- or more fundamentally, the function $\exp$ -- as its own thing, that in special cases can be interpreted as repeated multiplication, thanks to the functional relation $\exp(a)\exp(b) = \exp(a + b)$.

2015年2月3日 · I was wondering, what is the order of operations when it comes to multi level exponents. Couldn't find anything in google.

2020年12月5日 · Exponentiation is similar to functions in general in that they can both be represented as ordered pairs. In lambda calculus, the standard algorithmic definition of exponentiation is $\lambda be.eb$ , which is literally just defining it as a function and is by far the simplest mathematical operation in Church encoding.

While this would make things more convenient for us, exponentiation, unfortunately, does not work like this. For example: $(1+1)^2 = 4$ but $1^2 + 1^2 = 2$. Recall that, for multiplication, it is often easier to think of complex numbers in terms of argument (angle from the real axis) and magnitude (distance from zero).