this reminds me of when he said something about preserving differentiability, and I honestly don't know if that preserves it or not, but he did say that taking the absolute value (a similar thing to floor and ceiling) does not preserve it.
@@gtziavelis Yes it's about differentiability. When working with a series we have tests regarding integration so having a sequence defined as something continuous is important. The ceiling function, and also the absolute value are not differentiable for all x's in their domain.
is there another formula for this that doesn't involve trigonometric functions? and without modulus operators and without the ceiling and floor operators?
What if you used unit step function for the 0,0,0,1,... Also to make it little more versatile, possible to try make 0,0,1,0,1,1,0,0,1,0,1,1,... or something different between each repeating part.
This is like magic
Wooo sequences!!!
is there any reason not to do the ceiling function instead of adding 1/2 and multiplying by 2/3? it seems easier to just do ⌈cos(n * 2 * π/3)⌉
this reminds me of when he said something about preserving differentiability, and I honestly don't know if that preserves it or not, but he did say that taking the absolute value (a similar thing to floor and ceiling) does not preserve it.
@@gtziavelis Yes it's about differentiability. When working with a series we have tests regarding integration so having a sequence defined as something continuous is important. The ceiling function, and also the absolute value are not differentiable for all x's in their domain.
Interesting.
isn't the last one clearer if written as √2sin(n*π/2 - π/4)? that way you're also showing that you start at π/4
Yeah, it makes more sense to simplify, IMO. I expected him to multiply out the inside and fix that, but then he didn't.
You should include one - sign in front
Yeah may be there are many ways to write the same thing
Nice
is there another formula for this that doesn't involve trigonometric functions? and without modulus operators and without the ceiling and floor operators?
What if you used unit step function for the 0,0,0,1,...
Also to make it little more versatile, possible to try make 0,0,1,0,1,1,0,0,1,0,1,1,... or something different between each repeating part.
1) (x%3==0)?1:0 or int(x%3==0)
Finally first.