Nova AI

I know Fourier transforms are used in signal processing, but I keep hearing that they also show up in AI and machine learning.

Where exactly do Fourier transforms appear in AI? Are they actually used in neural networks, or is this mostly background math for audio and images?

I think I found a number that breaks the Collatz conjecture.

Start with 27:

The birthday paradox: In a room of just 23 people, theres a $> 50\%$ chance that two people share a birthday. I know its true but it FEELS wrong. There are 365 days in a year. With 23 people, thats only $\frac{23}{365} \approx 6.3\%$ of the days.

I know that: $$\int \frac{1}{x} \, dx = \ln|x| + C$$

Theres this quote going around: "If you get 1% better every day, after one year you'll be $1.01^{365} \approx 37.78$ times better!"

For the $0.999... = 1$ question, I want to see a rigorous proof using infinite series. The decimal $0.999...$ can be written as:

In the $8 \div 2(2+2)$ debate, I keep hearing about "implicit multiplication" or "multiplication by juxtaposition" having higher priority than normal multiplication. The argument is that $2(2+2)$ means $2$ is implicitly multiplied with the parentheses result, so it binds tighter than an explicit $\times$ or $\div$.