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  • What Is Exponentiation? - Mathematics Stack Exchange
    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
  • notation - What is the name of the answer to exponentiation . . .
    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 $3^2=9$
  • exponentiation - Whats the inverse operation of exponents . . .
    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
  • exponentiation - Prove that $i^i$ is a real number - Mathematics Stack . . .
    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
  • arithmetic - Why does exponentiation have 2 inverses? - Mathematics . . .
    So saying that "subtraction is the inverse of addition" is a bit sloppy, as you can see To even speak of inverses, you have to formulate addition and subtraction in a manner that makes them invertible The same is true of exponentiation And once you do this, it becomes clear that there is only one inverse for exponentiation, which is the
  • exponentiation - How do I reverse engineer this power of exponent . . .
    The short answer is "take logs" The logarithm, or log, of a number reflects what power you need to raise a certain base to in order to get that number
  • How to Understand the Definition of Cardinal Exponentiation
    When you say "normal exponentiation", you can think about natural numbers, real numbers, complex numbers, and so on Assuming that you mean natural numbers, we want a coherent behavior from infinite sets to the laws we have figured out on finite sets
  • 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





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