Thanks for this! I guess i need to read up on Hilbert Space.

...and Shor's Algorithm

Don't let the terminology intimidate you. The interesting ideas in quantum computing are far more dependent upon a foundation in linear algebra rather than a foundation in mathematical analysis.

When I started out, I was under the assumption that I had to understand at least the undergraduate real analysis curriculum before I could grasp quantum algorithms. In reality, for the main QC algorithms you see discussed, you don't need to understand completeness; you can just treat a Hilbert space as a finite-dimensional vector space with a complex inner product.

For those unfamiliar with said concepts from linear algebra, there is a playlist [1] often recommended here which discusses them thoroughly.

[1] https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...