24 июн. 2023 г. · I know that you can also define e as the sum of an infinite series. I believe it's the sum of 1 over n factorial from 0 to infinity, or ...

3 апр. 2022 г. · A definition cannot be proven. You can show equivalency or some implication. And the most important thing for me: write some text inbetween ...

29 июл. 2022 г. · e is the unique number satisfying ex ≥ x+1 for all real (alternatively, for all rational) x. This definition pins down e without using calculus.

25 июн. 2019 г. · E is literally the value of A, such that A^x=d/dx(A^x). This however is a definition based upon the derivative of a function of e rather than e ...

2 июн. 2024 г. · You can't prove a definition of a number. The only thing that you can prove is the convergence of the sequence/continuity of the function that ...

26 окт. 2023 г. · You need to prove that ((1+x)-1)/x approaches 1 (trivial) and (1/(1-x)-1)/x approaches 1 (it is equal to 1/(1-x)). Then you invoke the squeeze theorem.

17 окт. 2020 г. · You have to define ex and ln(x) somehow. Generally, you pick one of the relevant properties and use it to prove the others. You can pick any of ...

30 июн. 2018 г. · One way to define it (albeit not a particularly satisfying one) is to just let ex+iy = ex(cos(y)+isin(y)), in which case Euler's identity is ...

13 окт. 2024 г. · A valid definition for e is the unique real number that has an exponential function whose derivative is itself.

5 февр. 2024 г. · This might sound strange, but often mathematicians DEFINE the exponential ex as the function which is its own derivative.