I've recently learned that the cardinality of the integers and that of the rationals is the same, as you can map the rationals to the integer grid, draw a spiral that eventually touches every point and label from the centre outwards. If I understand it correctly, this is equivalent to saying that there's a bijective map between $\mathbb{N}^2$ and $\mathbb{N}$.
My question is, is there an extension to this idea that has a bijective map between tuples of integers of any size and single integers? For the 3rd dimension I can envision some kind of system with concentric cubic shells, but I can't visualise anything higher than that.
Please note that I'm not formally trained in math. I enjoy learning math on YouTube recreationally but I'll struggle to read denser notation.