I'd like to understand this better, if anyone can help.

[LionKing]

A number divided by zero is not zero, though. Approaches infinity.
https://en.m.wikipedia.org/wiki/Division_by_zero

A number divided by zero is "undefined". Infinity is a number too large to represent. Not the same thing.

But let us consider this:

I bake a cake. I tell my friends to come over and divide it equally amongst themselves. They never do. By this logic, a/0=a.

I did not say it is infinity. I said it approaches infinity, meaning that x/b approaches infinity as b approaches zero. The final destination is undefined. You wrote it is zero.

I really did not follow the rest, just noticed that one bit was not correct, so it would likely affect your deductions. I seem to remember something about mass approaching infinity as a particle is trying to reach the speed of light, therefore approaching a requirement of infinite acceleration to reach the speed of light (f=ma), meaning that you cannot ever reach it... But yeah, distant memories.