Hey guys, I suck at math. Suppose I wanted to construct a function

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x+sin(x)

Define it piecewise or use some step punction fuckery.

>>9074154
f(x)= x + (literally any periodic function that ranges from -1 to 1)

>>9074220
here's an example, plug this into wolfram alpha to get a less smooth version of this >>9074171

2/pi*arcsin(sin(pi*x))+2x

>>9074224

[math]\sum\limits_{0\leq k \leq n}{(k\ \bmod\ n)}[/math]

This will give you an integer sequence

>>9074224
how did you come up with that?

>>9074622

I fucked it up

this uses a predicate, expressed by square brackets

I guess you could use this for real n

[math]n -\sum\limits_{0 \leq k \leq n}{[k\ \bmod\ a = 0]}[/math]

>>9074624
The expression arcsin(sin(pi*x)) evaluates sin(pi*x) before applying the arcsin. The result is that the expression won't just be equivalent to pi*x once sin(pi*x) reverses its direction of change at sin(pi/2) and sin(-pi/2); it'll be a cyclical expression. What you get is a triangle wave with a slope that changes from pi to -pi. By multiplying this expression by 2/pi, you get a triangle wave with a slope of ±2. When you add 2x to that triangle wave, it amplifies the +2-slope portions to have a slope of 4, and it attenuates the -2-slope portions to have a slope of 0. The result is a step function constructed from a triangle wave.

I suggest playing with Desmos if you're just interested in the relation of a function to its graph. It's faster than Wolfram and will update in real-time.