It’s not a paradox
It’s not a paradox. It’s very clearly understood by many, many people, just not you. A non-zero constant divided by zero is not infinity, it’s not negative infinity, it’s not 8, it’s not shoe. It’s nothing. There is no value. Dividing by zero has no value, it has no meaning.
You can’t just haphazardly define something divided by zero as infinity, because it’s not true. It’s not mathematically true (or even mathematically sensible), it’s not practically true. If you take 5 eggs, and divide them evenly among five people, how much does each person get? If each non-existent person gets 7 eggs, you still have no eggs total. If each non-existent person gets an infinite number of eggs, you still have no eggs total. There is no answer. The question doesn’t even make sense.
Doing identities with infinity don’t even make sense, anyways. What’s the reciprocal of infinity? It’s not infinity, because infinity divided by infinity can be ANYTHING. Just like infinity minus infinity…could be -8, could be 16/15.
Infinity isn’t a number, and when you try and treat it like it is, things break down. When you do math with infinity, you always have to tread carefully. There are special things that have to be done when dealing with infinity, like special proofs and stuff. When you treat infinity like it’s number, it becomes clear you have no idea what you’re talking about and you’re just talking out of your ass.
BTW, your fake, non-sensical identity for infinity times zero wrong. If your division by zero was done with five as the divisor, then five is zero times infinity. If it was done with -12 as a divisor, then -12 is zero times infinity. Just another reason you don’t do identities with infinity, and why anything divided by zero is not infinity.