I Believe The Universe Is Purely Mathematical

Again. That's why I said "semi-formal" proof. Your logical fallacy is the "Fallacy Fallacy," in which asserting that just because a claim has been poorly argued, a fallacy has been committed.

1) Resonant frequency is objectively a non-physical property. It's the number of times something cycles/vibrates per second. It isn't a physical property. It is but a measure that relates to a change in position over a change in time.

2) Think about it for a second. We know that the universe is made up of particles. Either these will have a finite decomposition state, or they won't. Do tell me what else they could be. The only other option is to argue that the particle doesn't exist at all, in which we know isn't quite applicable to our reality.

3) This is not what I am saying. An apple is still an apple, regardless of whether or not we've come along to name it as such. The apple has existed before we named it, and even if we haven't named the apple, it would still remain an apple. Because frankly, the apple doesn't care what people call it. It will still continue to exist as an apple. Our language of mathematics is merely a metaphor for what has always existed and explains our universe. Much like the apple, math doesn't care how we express it. A "two" is an inherent property. No matter what we call it as, or what we defined it as being--even if we used a completely different number system, "twoness" is an objective parameter. I have an apple here, and an apple there. Whatever term we describe to express the quantity of apples I have, I still have a fixed quantity of apples. I have three erasers on my desk right now. Even if we never discovered math, have never created a number system, or any mode of describing quantity, really, there is an inherent "threeness" involved in the quantity of erasers. I also have three SD cards on my desk. Not four, not two, but three. Again, there is this inherent "threeness" that exists with the quantity. No matter what we call it, o o o , how many o's are there? Whether or not it is called "three" or not, we know that there are the same number of o's as there are in r's in r r r. Mathematics is just our metaphor for the language of the universe. Much like our musical notes and the music staff is a metaphor for us to comprehend music and sound, mathematics is our language to explicitly define the universe. It is our way of understanding the universe. By naming the apple, we now have a means to communicate a message to a person and to understand the apple better, because all one has to do is mention "apple" and one gets an idea of what a person has in mind. Of course, we need to mention WHICH apple we're referring to, and we have no names for every single apple in existence. At the same token, we have no ways of reasonably mathematically describing every particle in existence. However, we know that apples have a general property across all apples. Apples are generally either red, yellow, or green. Apples are typically juicy. Apples generally all have the same shape. With this, we don't need to name each individual apple. Just every species of apple, because anything within the species are more or less identical in parameters. With particles, identical particles are 100% identical and share no variation.

Stuff isn't *explicitly* made of math. But stuff can only be mathematically defined. One would look at a complex fractal, and completely deny that it was mathematically generated with a relatively simple formula if they didn't know what a fractal was. The fractal itself isn't made up of math. But it is mathematically defined. Take my icon, for instance. It's the Mandelbrot Set fractal. Watch most zooms of it, and you'd completely deny that it was mathematically generated. But oh, no. All it is is taking points on the complex plane, plugging them into z=z²+z, fixating the constant, and feeding the output back into the squared term over and over again, and if the point stays within the bounds [-2,2,-2i,2i], it's in the Mandelbrot Set. The color is merely the speed of which the other colors approach infinity. Nothing more. So while the Mandelbrot Set image itself is not literally made up of math, it is mathematically defined as such. In the same way, our universe is like a fractal render. The render is inherently contained within the equation. What we "observe" is merely its render, whereas it doesn't change that there was a pure equation that generated it. Getting into observation of the render and the concept of observation is a completely different discussion that goes into philosophy and outside the realm of possibility though.

Now do you understand?

That's not quite what the "fallacy fallacy" means.
I'm not saying your conclusion is wrong because you have fallacies. I'm just trying to point out the fallacies lol.
Ultimately, it doesn't matter how great your proof sounds since, in the end, this is merely a thought experiment. Without any empirical data/evidence, you can't really prove anything. You can use math to predict outcomes or predict how something will work, but it's only proven when you actually put it to the test.
Fortunately, most of the mathematics we know and use every single day works just fine. It's actually really, really good at predicting pretty much everything that we can experience ourselves. We had to tune it to be that good though. It didn't always just work. The problem arises when we realize that our math can't do everything. It is still flawed. It does still break down when we apply it to certain situations in the universe. It obviously still needs things added to it (or completely redone for all I know) in order to accurately apply to everything in the universe. For this reason, it feels more like an invention to me than something intrinsic to the universe. It's a tool that we created in order to represent reality as closely as we possibly could. As I said, it's REALLY good at doing it, but definitely not perfect.
When you say the universe is purely mathematical before it even existed, maybe I'm just not even sure what you're even trying to say lol.
As for your boolean situation, I could be wrong, but that does sound like a false dichotomy to me. What sounds like an actual boolean situation is something like "Either the universe is ultimately made up of single particles, or it's NOT made up of single particles." If the universe isn't made up of single particles, that doesn't necessarily mean that it's made up of infinitely divisible ones, does it? If so, how do you deduce that exactly? Is there a source you can point me to if I'm just totally missing something?
Overall, I'm just a little unsure what your premise is supposed to mean when it claims that physical things are purely mathematical. Again, I apologize if I'm missing your point.

Also, thank you for taking the time to respond. I find this very interesting!

Oops, actually I just looked up the "fallacy fallacy", and you were right about what it is. My bad.

Well yeah, that's why this is a "semi-formal" proof. Our math can do everything. The only thing is, we simply don't know the parameters of every particle in the universe, in which causes minute differences in the final condition, even with the tiniest of changes in the initial parameters. So it's *our* inadequacy that our math isn't perfect. Both we need an unrealistic amount of data about literally *everything* there is to be 100% accurate, and also, it's a matter of time before we discover a branch of mathematics to explain it. People originally thought that no math outside of sacred geometry could describe nature, yet Benoit Mandelbrot came along in the 1970s and introduced fractal geometry, which was a *very* good representation of natural structures. Fractals have always existed. As with all math, we simply discover them, not invent them. We invent *ways* of *representing* them, but we didn't invent math itself; it is intrinsic and inherently encoded into everything. This is merely a theory, and theories require you to make assumptions. That's the entire part of a formal proof. So while technically I have made assumptions, my logic isn't flawed. If my assumptions were all correct, then my proof would hold. If my assumptions were not correct, then my proof would be unstable. You are, again, missing my point. Lets say there is this hypothetical circle that represents the universe, and each "pie slice" of it represents a fundamental particle. We know that the universe is cut up into at least n number of pie slices, as we can observe them with the LHC and TEM microscopes. Would you not agree that I can either have a finite number of pie slices, or an infinite number of pie slices, or have the pie sliced such that you only halve one of the previous halves (think of 1/2ⁿ * 360 to be the arc length of a circle with unit circumference, where n is the iterations done--the number of slices of a slice done )? Some combination of finitely wide slices and infinitesimally wide slices, or just one of the other? If there's another way to cut the circle such that you don't have either a finite number of slices or an infinite number of slices, or a combination of such, do tell me, as that could completely break our understanding of mathematics, regardless of what the universe is made up of. Do you understand now?