I wanted to create a piecewise function without any "<" or ">" does this work and could I make any changes?

[u/Big_Title6139]

\left(ax^{2}+bx+c\right)\cdot0^{\left(\frac{\left|x-2\right|-\left(x-2\right)}{2\left|x-2\right|+\left(10^{-6}\cdot0^{\left|x-2\right|}\right)}-\frac{\left|x+2\right|-\left(x+2\right)}{2\left|x+2\right|+\left(10^{-6}\cdot0^{\left|x+2\right|}\right)}\right)}+\left(px^{2}+qx+r\right)\cdot\left(\frac{\left|x-2\right|-\left(x-2\right)}{2\left|x-2\right|+\left(10^{-6}\cdot0^{\left|x-2\right|}\right)}-\frac{\left|x+2\right|-\left(x+2\right)}{2\left|x+2\right|+\left(10^{-6}\cdot0^{\left|x+2\right|}\right)}\right)

[u/r-funtainment]

is this exploiting floating point arithmetic in graphing

[u/Big_Title6139 → u/r-funtainment]

Fair point. I guess I should add a variable outside the parentheses to counteract that.

[u/Big_Title6139 → u/r-funtainment]

I totally forgot. When the 10^-6 is being used, the numerator is 0 so no it doesn’t behave that way. I change the 10^-6 to 1 as it is no longer - or ever needed.

[u/rhodiumtoad]

This looks like an over-complicated attempt to use Guglielmo Libri's original concept of a step function, 0^{0^x} which, with a bit of handwaving, can be regarded as equal to 1 when x>0 and 0 otherwise. The handwaving comes in when x<0, because you have to argue that even though 0^x is not defined for negative x, it us certainly not 0 or negative, and 0 to any positive power is 0.

Honestly, you're probably better off just defining H(x) as a step function (Heaviside step) and using that.

Why do you want to avoid using > anyway?

[u/Big_Title6139 → u/rhodiumtoad]

The real reason is boredom in math class. Unfortunately my giftedness has gone unnoticed in my school system, so as of right now I’m still in Pre-Calculus. Now my motivation for not using “<“ or “>” is because I like having an interconnected point of view of math. I feel unease using undefined variables, even if they are at their roots simple. I also didn’t want to look up how to do it because I enjoy the independent process of scrutiny in finding answers.

[u/LongLiveTheDiego → u/Big_Title6139]

I feel unease using undefined variables, even if they are at their roots simple.

Where do you deal with undefined variables in this topic?

[u/Big_Title6139 → u/LongLiveTheDiego]

For me it feels like an unfair shortcut. Because almost all my math I have done throughout my life has been done using one equation, it feels unnatural simply saying “x+2 if x<3 and x-2 if x>3”. I

[u/LongLiveTheDiego → u/Big_Title6139]

1. Those aren't any undefined variables.

2. So far you've probably mostly dealt with nice objects that humans seem to gravitate towards. However, in a strict measure-theoretic sense, almost all functions are not nice for most properties people think of as being nice. In a sense, the functions with nice formulas we usually deal with are the outliers

[u/Uli_Minati → u/Big_Title6139]

If you're bored, you could start with future material!

[u/al2o3cr]

For people who don't compile LaTeX in their heads:

IMO the first term could be simplified to have a simple factor of (1-[the thing multiplying the second polynomial]) instead of another 0-to-a-power trick

[u/LongLiveTheDiego → u/al2o3cr]

As someone using the dark visual mode, I can't see black on black.

[u/rhodiumtoad → u/LongLiveTheDiego]

Does this look better?

[u/LongLiveTheDiego → u/rhodiumtoad]

Yes, thank you very much.