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Old 2022-06-24, 21:22   #12
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Originally Posted by x13420x View Post
Yes thank you

11^0/0! + 11^1/1! + 11^2/2!....... I believe this is transendental but now that I think about it I think it will go to infinity......I am doubting that this converges on a number....sorry seems I am babbling now....
I think it does converge. The terms approach 0 as n goes to infinity. I can quite make subsets of terms be bounded and making the subset sum less then some bound which clearly is by experimentation with PARI/GP. It is less than 59875. We need an analyst to step in.

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Old 2022-06-24, 21:40   #13
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I think it does converge. The terms approach 0 as n goes to infinity. I can quite make subsets of terms be bounded and making the subset sum less then some bound which clearly is by experimentation with PARI/GP. It is less than 59875. We need an analyst to step in.

This is the definition of e^11...
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Old 2022-06-24, 21:46   #14
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This is the definition of e^11...
I have forgotten how to prove e is transcendental. Intuitively, it cannot be written algabraically. Without me referring to my Spivak book, can you explain how it is proven transcendental? e^11 is not infinite.

Last fiddled with by paulunderwood on 2022-06-24 at 21:48
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Old 2022-06-24, 21:58   #15
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I have forgotten how to prove e is transcendental.


https://en.wikipedia.org/wiki/Transc...transcendental
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Old 2022-06-24, 22:28   #16
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For my next tricks, I have forgotten how to prove pi is transcendental, the proof of Prime Number Theorem and have never quite figured out the proof of Riemann's Hypothesis.

Last fiddled with by paulunderwood on 2022-06-24 at 22:31
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Old 2022-06-24, 22:36   #17
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For my next tricks, I have forgotten how to prove pi is transcendental, the proof of Prime Number Theorem and have never quite figured out the proof of Riemann's Hypothesis.


You might have got this confused with the proof that e is irrational, which is much simpler - I seem to recall being set it as an exercise as a first-year undergraduate.
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Old 2022-06-25, 04:48   #18
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Originally Posted by x13420x View Post
Did you guys notice when you add the 2 results you get the modulo number plus 1? like 8 + 4 = 11 + 1
Yes, that is expected.

sqr(n) has positive and negative roots, so sqr(n) mod x will be have roots y and x-y. (sqr(n) + 1)/2 + (-sqr(n) + 1)/2 = 1
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Old 2022-06-25, 10:03   #19
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yes e^11 = 59874.14171519782

https://onecompiler.com/python/3y84dfvhf
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Old 2022-06-25, 11:21   #20
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Would the square root of 2 be an imaginary number?
√2 ≡ 3i ≡ 8i (mod 11)
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Old 2022-06-25, 20:24   #21
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Did you guys notice when you add the 2 results you get the modulo number plus 1? like 8 + 4 = 11 + 1
Yeah isn’t that called a multiplicative inverse? (Or am I confusing things) the number x such that ax ≡ 1 (mod n)
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Old 2022-06-25, 20:31   #22
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Yeah isn’t that called a multiplicative inverse? (Or am I confusing things) the number x such that ax ≡ 1 (mod n)
The additive inverse....
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