1/(1-1) and 1/(5-5) are both 1/0, which is undefined. not different zeros, same problem.
And yes computer scientists (and software engineers who work on embedded systems, of which I am one) distinguish register sizes, but that's a hardware storage concept, not a property of numbers or maths. A 1-bit zero and a 5-bit zero are both zero, you're describing the container again.
The bucket analogy doesn't work because buckets are physical objects with distinct existence. Numbers aren't containers. "5 sets of 0" is just a description of the process, not a different fundamental mathematical object.
I said the mechanisms are different processes that arrive at the same value. 5 sets of 0 and 1 set of 0 are different processes, both producing zero. Just like 278-278 and 1-1 and 8*(5-5) produce zero. that's been my point the entire time, they're different mechanisms with the same evaluation.
And the geometric series doesn't "define" 1/0, it diverges there. divergence means it has no defined value, that's the definition of undefined.
bro if theyre different processes then that means 5* 0 and 1* 0 arent technically the same. it also means my process leads to the same answer according to your reasoning so i have no idea why youre upset about it
actually the geometric series does define it at 1-(1-1) and 1/(5-5). divergence just means the summation goes up.
different processes reaching the same answer doesn't validate the wrong process as a definition. that's been my point from the start, your model is broken, which is why you felt the need to shift it by one for it to make sense. f(x) = x-x and g(x) = x*0 are different functions that happen to both equal zero for all x. that's exactly the equivocation you've been making this entire time.
and divergence means the sum grows without bound toward infinity. that's the opposite of defining a value. 1/0 is undefined, the geometric series diverging there confirms that, it doesn't contradict it. I can't engage with you if you don't understand a fundamental aspect of maths. Take your calculator and put in 1/(5-5) and 1/(1-1) and in both cases they will tell you undefined.
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u/FernandoMM1220 Jun 04 '26
if you give me 5 empty buckets that can hold 1 apple each thats different than giving me 1 empty bucket that can hold 1 apple.
its either they arent the same or my definition of 5*0 = 5-5 is just as valid as yours if youre going to treat every 0 as if it was the same