Comments by "Samuel De Andrade" (@samueldeandrade8535) on "The Math Sorcerer" channel.

  1. Not including answers in Math books always was a dumb decision.
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  2. It is pretty fun. And based on such a simple idea.
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  3. Oooh really??? That seems interesting ... Will check your recommendation right now.
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  4.  @TheNetkrot  "I have seen it done but can't find it again". Yep, I can say the same thing. Several proofs I saw involve circular reasoning. I guess the following is valid: 1) Prove the limit lim (e^h - 1)/h = 1 when h goes to 0. This is actually the derivative of e^x in the point 0, or (e^x)'(0). For that we invoke the supreme and original definition of e: e = lim (1+1/n)^n when n goes to infinity. This implies e = 1/0! + 1/1! + 1/2! + 1/3! + ... e^x = lim (1+x/n)^n e^x = 1 + x/1! + x²/2! + x³/3! + ... So, using this last one, which is e^x's power series, which I said it is implied by the supreme and original definition of e, we have lim (e^h - 1)/h = lim (1 + h/1! + h²/2! + h³/3! + ... - 1)/h = lim (h/1! + h²/2! + h³/3! + ... )/h = lim 1/1! + h/2! + h²/3! + ... = 1 Ok? First part done. 2) Prove (e^x)' = e^x Well, by definition if derivative of a function, (e^x)' = lim (e^(x+h) - e^x)/h = lim (e^x e^h - e^x)/h = lim e^x(e^h - 1)/h = e^x lim (e^h - 1)/h = e^x 1 = e^x That's it. I think it is valid.
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  5. Disappointing, huh?
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  6.  @julianwilson9919  oh my Euler ... thank you very much again. That day I got sad because I couldn't find the book anywhere. I just saw your reply, tried again and found it!!! There are Excerpts about mathematicians!!! Yaaay! I don't know where I will start, but definitely not at page 1. I am a little wild. Hahahahahaha. I guess I will start at 12. Number Theory ... page 273 Thank you!
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  7.  @TheNetkrot  the Taylor approximation of e^x can be obtained from its definition.
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  8. It looks like a great book. The cover image is brilliant.
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  9. What? You really are confused.
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  10. Meh. Not true.
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  11. ​@pinklady7184 you have no idea what Sudoku has become to say something like that. Sudoku today is pratically a branch of Math.
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  12. Nope.
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  13.  @julianwilson9919  because I just woke up, I guess I am feeling tamed and started at page 1, The Breakthrough, and now I have a favorite cubic equation (which I love) and a favorite representation of 2: x³+6x-20=0 that has solution given by the cubic formula ³√(√108+10) - ³√(√108-10) a funny way to write 2! I have to drink coffee. And do things before reading this book. Hahaha.
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  14. That's not the "fundamental idea". That's the definition of derivative.
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  15.  @TheNetkrot  you may ask me what I know you want to ask. Hahahaha.
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  16.  @TheNetkrot  so you mean avoiding the Taylor series? Well, maybe I saw it. Not sure. If I have time in the next days, we could figure it out. Shouldn't be that complicated.
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  17.  @TheNetkrot  man, as I said, the expression e = 1/0! + 1/1! + 1/2! + ... and the Taylor series comes from the limit definition. Let me wake up and take my breakfast and I will show it.
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  18. Man, this is easy. Now do it with the product. The limit point and the limit of the product being a real number (not infinity).
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  19. What do you mean?
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  20. That's ... not good advice. I will explain why soon.
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  21. How delusional.
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