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.
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.
0ops@lemm.ee 9 months ago
Our minds? Infinity isn’t something we don’t understand - we invented the concept of infinity. The mathematics community agreed on its definition, which includes the fact that infinity is not a real number, it literally does not exist. Show me infinity, I’ll give you infinity+1.
You deciding that infinity means something else is not a math problem but a language problem, so if being right about this is that important to you, start a petition or something
MacGuffin94@lemmy.world 9 months ago
It is explicitly not a value. The reason you cannot perform arithmetic on infinity is because it has no value. It has cardinality but that is not unique. The set of all integers is infinite as is the set of all real numbers but they have different cardinality as integers are countably infinite whereas real numbers are not countable infinite.
FooBarrington@lemmy.world 9 months ago
No, it’s not a value. It’s defined as not being a value. No after how much you bend and break maths, infinity will never be a value. Why do you keep telling people wrong things?
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…
0ops@lemm.ee 9 months ago
It breaks calculus, the math that made your phone and has a billion other uses. Directionality of infinities is critical. In calculus, infinity refers only to the magnitude of the resulting vector. Because I suspect you don’t know, integers are a 1-dimensional vector.
FooBarrington@lemmy.world 9 months ago
Okay, so what? Breaking useful things is bad, no matter what group they belong to. What is positive about no longer being able to use L’Hopital’s rule?
magic_lobster_party@kbin.social 9 months ago
Infinite is not calculable math. If you use infinity in your calculations you will get slapped on the wrists by a math professor.