I saw this Reddit post today saying "My son's third-grade teacher taught my son that 1 divided by 0 is 0. I wrote her an email to tell her that it is not 0. ...
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.
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.
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
First sentence from Wikipedia: “Infinity is something which is boundless, endless, or larger than any natural number.”
In other terms give me a natural number n, I’ll show you a larger number, n+1, and I’ll do it again and again. That’s the definition of infinity. There’s always a bigger number.
Right! hence why you can only approach it with the limit notation, never operate on it directly. Please, take a calculus class. You might even learn this on day 1
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?
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.
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.
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.
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
So you believe the universe just ends somewhere with nothing behind it?
What’s that got to do with anything? Infinity is just shorthand for “ever-increasing number”.
Uhm… No it’s not… 🤨
First sentence from Wikipedia: “Infinity is something which is boundless, endless, or larger than any natural number.”
In other terms give me a natural number n, I’ll show you a larger number, n+1, and I’ll do it again and again. That’s the definition of infinity. There’s always a bigger number.
Boundless and endless (and the fact it’s larger than any number) doesn’t mean it’s ever-growing. It already is.
Right! hence why you can only approach it with the limit notation, never operate on it directly. Please, take a calculus class. You might even learn this on day 1
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?
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.