2014年3月8日 · Exponentiation is related to growth that is always proportional to how large the quantity has grown so far. You can have different starts and rates but you can imagine the growth as happening gradually and continuously, and imagining how that would interpolate is how you extend to reals.

2016年10月10日 · If I know the outcome of a value being raised to a certain power, is it possible to know what the original base was? Example: x ^ 0.25 = 2.5045 What's the proper way to calculate x?

A pedantic point: is a complex number with a 0 imaginary part the same as a real number?

Exponentiation is not associative, and it shouldn't be, because in many more general cases its two inputs are different types of things. Therefore, there's no reason to expect repeated exponentiation to have any reasonable properties along the lines of the natural and useful homomorphism properties of multiplication and exponentiation, and as ...

The way that I was taught it in 8th grade algebra, a number raised to a fractional exponent, i.e. ax y is equivalent to the denominatorth root of the number raised to the numerator, i.e. y√ax. So what happens when you raise a number to an irrational number? Obviously it is not so simple to break it down like above. Does an irrational exponent still have a well formed meaning? The only ...

2024年9月23日 · I was reading about exponentiation in lambda calculus on Wikipedia and found the expression \\begin{equation} \\lambda x. \\lambda y. y\\; x \\end{equation} and on the Church encoding page it states \\be...

2017年4月25日 · The definition of the exponential with integer exponents is straightforward to define: xn = x ⋅ … ⋅ x n−times x n = x ⋅ … ⋅ x ⏟ n − times. These days I've been thinking about the formal definition of the exponential with real exponents. My question: What is the definition of ab a b, where a, b ∈ R a, b ∈ R.

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...

You can demonstrate quite easily that given natural numbers m, n that the cardinal exponent nm agrees with the usual arithmetic one (with the slight quibble that the definition of cardinal exponentiation gives 00 = 1, which is, at times, left undefined in ordinary arithmetic).

2016年10月7日 · I'm rather familiar with exponents, I know that , but what if the exponent is less than one, how would that work? I put in my computer 251 / 2 anyway, expecting it to give me an error, and I got an answer!! And even more surprising, when I did this with more numbers and a little research, I found that x1 / y = y√x