I was always taught it was infinity as opposed to impossible.
doctorn@r.nf 9 months ago
Anything /0 is considered impossible as an agreement. There’s no actual math involved in that answer. In reality you can divide by 0, but the answer has no natural number.
How many times can you add 0 before you get 1? The answer actually is the drunk(😅) 8 or ‘infinite’, but our minds can’t grasp the very existence of infinite, so we just went with ‘impossible’.
There are ways to circumvent that added concept of some calculators when dividing by 0 anyway and it will show you “Infinite” if it is able to. I remember you could do this in C+ even, but not 100% sure anymore how. I think it was with dividing by an ever decreasing number-variable. When it reaches 0 just before the calculation, C+ didn’t default to an error, but just said ‘Infinite’. But like I said, not 100% sure anymore if that was the actual way.
HubertManne@kbin.social 9 months ago
addie@feddit.uk 9 months ago
Division is defined as the inverse of multiplication. The answer to one divided by zero is the same as asking which number you would multiply by zero in order to get one. No number has that property, not even infinity. So the answer is undefined.
One divided by ‘epsilon’, where epsilon represents a very tiny number, approaches infinity for ever tinier epsilons, so in some maths contexts infinity makes sense. But in general it’s a meaningless question, and so can only have a meaningless answer.
0ops@lemm.ee 9 months ago
If your counter against that is that 0 will never become 1 no matter how many you add, then that just proves ‘infinite’ correct. If it ever could, it wouldn’t be infinite…
You’re confusing infinity for unreal numbers. Infinity and negative infinity are not real numbers, but not all unreal numbers are infinity or negative infinity.
If you’re strictly adding zeros, then adding infinite zeros nets you zero. If adding zero once didn’t change the result, then adding it infinite times won’t either. If you need to add enough zeros to get to 1, that number doesn’t exist - but that doesn’t mean that it’s infinity, it means that there’s no solution. Infinity is a placeholder for “larger a real number than you can imagine”, but when you multiply that by zero, the magnitude of infinity is a moot point because you have zero infinities.
In calculus if you’re curious, you’re usually not strictly adding zero itself like above but instead adding values that approach zero. In that case, 0*infinity really “a very small number times a really big number”, and that is called an “indeterminate form”. In that case you may try rearranging it to solve
doctorn@r.nf 9 months ago
You say it yourself. If you jeep adding infinite zeros you will never get 1, hence the ‘divided by 0’ part.
Also, 0 is technically not a number either, it’s the concept of the absence of one. You can’t count 0 things. That doesn’t mean we don’t use it, thogh. It’s just less hard to imagine and closer to our basic calculations than infinity is.
0ops@lemm.ee 9 months ago
Zero is a real number, but not a natural number. I’m not going to explain the difference because, dude, this is junior high math
doctorn@r.nf 9 months ago
Indeed, and infinite isn’t… It’s like comparing Newton and Einstein on a regular earth scale.
Ferris@infosec.pub 9 months ago
the limit of y in 1/x=y as x approaches 0 from negative one is negative infinity. the limit as x approaches 0 from positive one is positive infinity. 1/0 is simultaneously both positive and negative infinity and is paradoxical.
doctorn@r.nf 9 months ago
One could argue that negative and possitive infinity, unlike natural numbers, boils down to the same thing, though. Just like 0, infinity technically has no + ir -.
MacGuffin94@lemmy.world 9 months ago
Don’t think of infinity as a value. It’s more of a concept to explain numerical behavior. What you described would be like running north at 5 mph south. The limit diverge do it does not exist.
doctorn@r.nf 9 months ago
But it is a value. Just one we tend to avoid by claiming it doesn’t exist or is impossible… Our minds just have a hard time imagining it, but that doesn’t mean it doesn’t exist.
FooBarrington@lemmy.world 9 months ago
If you were to argue this, you’d suddenly break a lot of useful maths. So why would you do so?
doctorn@r.nf 9 months ago
I’d only break argumentative math, not actual calculatable math…
Unlike many always say, math has too many agreements and ‘definitions’ and things we added to be universal. On a universal level infinite solves the +/- by the fact it’s infinite…