Recent content by why Fenix

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    Roots of series of exponential raised to power of x?

    so at first post you wanted to solve something like this? a1e(1+2f)x+a2e(1+f)x+a3e(2+f)x+a4efx+a5ex=0 by ##e^z=\sum_{n=0}^{\infty} \frac{z^n}{n!}## we get ##\sum_{n=0}^{\infty} \frac{a_1((1+2f)x)^n+a_2((1+f)x)^n+a_3((2+f)x)^n+a_4(fx)^n+a_5x^n}{n!}=0## ##\sum_{n=0}^{\infty}...
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    My simple proof of x^0=1 part 2 (axioms)

    Ad.2. For x≠0 we get from (M5) that ##x^{-1}## exists. Ad.1. I think i will get it from 3) Ad.3. Is given for positive natural a,b, in Remark 1.13. For negative a,b we can get it from remark 1.13 and (equation1 --- x-1x-1=x-2 extended to (k-times) x-1x-1⋅...⋅x-1 =x-k). Now we can take...
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    My simple proof of x^0=1 part 2 (axioms)

    yes, you are right. 1 = 0/0 = ((1+1) * 0)/0 = (1+1)*(0/0) = (1+1) and would be 0=1. and we got zero ring... http://en.wikipedia.org/wiki/Zero_ringBut main thing in this post is the proof that x^0=1. for x≠0. In any field. Is it good?
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    My simple proof of x^0=1 part 2 (axioms)

    When you start from axioms and wonder about x0=1 you can show that x0=1 for x≠0 because of (M5). (As I did in my first post above.) So when you extend (M5) with (1/0)=∞, like it is done in Riemann sphere, you should get what x0 for x=0 is. Thanks to (M5) with (1/0)=∞ for x=0 we get from (M5)...
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    My simple proof of x^0=1 part 2 (axioms)

    As I said. We are not in real numbers or extended real numbers. But in ℂ∪{∞} or something like Riemann sphere. Here http://en.wikipedia.org/wiki/Riemann_sphere you can find "...The extended complex numbers are useful in complex analysis because they allow for division by zero in some...
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    Roots of series of exponential raised to power of x?

    Because people making examples, problems, tasks, are not monsters, and usually polynomials have integer roots like {0,1,-1,2,-2,3,-3} or √2 or it combination with irrational i, that you can guess, or get close to guessing by looking at derivatives and how function is running. Polynomial of 5th...
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    My simple proof of x^0=1 part 2 (axioms)

    Yes. Proof is finished on "the end...". I was just trying too write something funny in the end of the post... :) But now I wonder. Let us assume that we are in Riemann sphere or just ℂ∪{∞} and (M5) is given for (X=0) by 1/0=∞. Of course ∞=z*∞=z*1/0=z/0. and now we will get 00=0/0 (of course we...
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    My simple proof of x^0=1 part 2 (axioms)

    I was looking for explanation why x^0=1. thread https://www.physicsforums.com/threads/my-simple-proof-of-x-0-1.172073/ is locked and i did't found solution in it from axioms. People using exp(x) and log(x) and xa-a=xax-a as given. If you have xa-a=xax-a for a∈ℤ and x∈ℕ+ then there is no...
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    Roots of series of exponential raised to power of x?

    Let y=ex then e-kix=y-ki you get a1y-k1+a2y-k2+...+any-kn =0 or for z=1/y=1/e-x a1zk1+a2zk2+...+anzkn =0 you got polynomial.now ask yourself about x5-x-1=0 go here http://en.wikipedia.org/wiki/Galois_theory to section "A non-solvable quintic example"
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