Extraordinary of this system is, you dont just compare LHS=RHS, you also compare the Total magnitude on RHS is equal to LHS making it more strong in its stability and more aligned to this world as physics also says the same, the energy is always conserved, and here, magnitude is always conserved.
I may have not accurately understood question however Ill answer as per what I have understood meanwhile I also suggest to check fundamentals of universal Numbers in this channel. Its 7 minute video. I believe that basic can be used to derive any part of mathematics as per universal number. Coming to what I understood "what about zero in finite field". I would say 0 has no use if number line is not willing to go in depths till infinite fields but it also looses its associated advantages. Its same way pi and e has no use in natural number if real number don't exist, Minimum required framework precision is real number for Pi and e or root 2. Without logic of real number, we cannot identify if 3.2 is greater then 3.1. And point at infinity can be understood from this video(Its same fundamental video) ruclips.net/video/dpE8E3Ld3HY/видео.html
Extraordinary of this system is, you dont just compare LHS=RHS, you also compare the Total magnitude on RHS is equal to LHS making it more strong in its stability and more aligned to this world as physics also says the same, the energy is always conserved, and here, magnitude is always conserved.
What about zero in finite fields and points at infinity on algebraic curves?
I may have not accurately understood question however Ill answer as per what I have understood meanwhile I also suggest to check fundamentals of universal Numbers in this channel. Its 7 minute video. I believe that basic can be used to derive any part of mathematics as per universal number.
Coming to what I understood "what about zero in finite field". I would say 0 has no use if number line is not willing to go in depths till infinite fields but it also looses its associated advantages. Its same way pi and e has no use in natural number if real number don't exist, Minimum required framework precision is real number for Pi and e or root 2. Without logic of real number, we cannot identify if 3.2 is greater then 3.1.
And point at infinity can be understood from this video(Its same fundamental video)
ruclips.net/video/dpE8E3Ld3HY/видео.html