- #1
kulix
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Just a quick question for you guys, I've been unable to find the answer to this. Can all real numbers be written as n^p, where p is a real number?
kulix said:if n < n * sqrt(n^2-1) < n^2, does that mean there exists p such that n * sqrt (n^2 -1) = n^p ?
kulix said:Oh dear. Let me try this:
let S be a series from 2 to infinity of 1 / (n*sqrt(n^2 -1)).
Can you write S as 1/n^p?
Real numbers as powers of real exponents are numbers that can be expressed as a base number raised to an exponent, where both the base and the exponent are real numbers. This notation is often used to represent numbers that are too large or too small to be written out in standard decimal form.
To read a real number as a power of a real exponent, you say the base number followed by the word "to the power of" and then the exponent. For example, 10 to the power of 3 would be read as "10 to the power of 3" or "10 cubed".
A real number is any number that can be found on the number line, including integers, fractions, decimals, and irrational numbers. A real exponent, on the other hand, is a number that is used to represent repeated multiplication of a base number by itself. It is often written as a superscript to the base number, such as 5³.
Yes, real numbers can be raised to any real exponent. This includes positive exponents, negative exponents, and fractional exponents. However, some combinations of base numbers and real exponents may result in complex numbers, which include both a real and imaginary component.
Real numbers as powers of real exponents are useful in science because they allow us to represent very large or very small quantities in a more compact and manageable way. This notation is often used in fields such as physics, chemistry, and biology to represent values such as distances, masses, and concentrations.