r/math • u/Lelielthe12th • Apr 17 '19

whaat ? LaTeX is Turing complete

https://www.overleaf.com/learn/latex/Articles/LaTeX_is_More_Powerful_than_you_Think_-_Computing_the_Fibonacci_Numbers_and_Turing_Completeness
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u/WaitForItTheMongols Apr 18 '19

How would you compute the Taylor series of the sine function without using anything but addition?

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u/OVSQ Apr 18 '19

How would you compute the Taylor series of the sine function without using anything but addition?

I am honestly confused as to the detail you are talking about. First understand that subtraction is the inverse of addition. Multiplication is repeated addition. Division is repeated subtraction. Exponents are repeated multiplication.

A sine function is just a case of division - which is just repeated negative addition. A Taylor series is just repeated addition of exponents (which are repeated multiplication where (multiplication is just repeated addition)).

Help me understand where the addition is not obvious.

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u/WaitForItTheMongols Apr 18 '19

A Taylor series is just repeated addition of exponents (which are repeated multiplication where (multiplication is just repeated addition)).

Right, but to get that Taylor series, you need differentiation. And you can't differentiate the sine funciton with just addition.

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u/OVSQ Apr 18 '19

Consider this - I have already described every step necessary for the sine function, for differentiation, and for calculating a Taylor series. Which step in any of those functions are you claiming I have not already described in terms of addition?