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. ...
We do have a concept of limits in math. That doesn’t mean we ignore it. It is just more correct not to divide by zero as the limits from either side do not converge. Or would you allow -inf as an answer aswell? That is the answer if we approach the limit from the other side.
It is not only convenience but rigor that dictates dividing by 0 to be an erroneus assumption.
It was drilled into my head in school that it’s not a proper limit unless it includes the text “lim A->B”. So using infinity at all, without specifying that you’re taking the limit, would be incorrect. This makes sense as infinity isn’t a real number that you can actually be “equal to”, just a concept you can approach, so you need to specify that by taking the limit, you’re only approaching infinity. I guess the guy you’re replying to needs to hear this more than you though.
One positive infinity doesn’t even necessarily equal another positive infinity, as two expressions might not approach infinity at the same rate. Note the word “approach”. That’s the only way you’re allowed to use infinity/-infinity, by approaching it. It’s not a real number, it doesn’t actually exist. Second, in most contexts (calculus) it strictly refers to magnitude (ie, it can have directionality applied to it). Take a calculus class if you want to learn more.
We do have a concept of limits in math. That doesn’t mean we ignore it. It is just more correct not to divide by zero as the limits from either side do not converge. Or would you allow -inf as an answer aswell? That is the answer if we approach the limit from the other side.
It is not only convenience but rigor that dictates dividing by 0 to be an erroneus assumption.
It was drilled into my head in school that it’s not a proper limit unless it includes the text “lim A->B”. So using infinity at all, without specifying that you’re taking the limit, would be incorrect. This makes sense as infinity isn’t a real number that you can actually be “equal to”, just a concept you can approach, so you need to specify that by taking the limit, you’re only approaching infinity. I guess the guy you’re replying to needs to hear this more than you though.
Infinite, just like 0, actually has no - or +. So yes and no. For all intents and purposes -inf == inf.
This is completely wrong, please don’t listen to this person.
I suggest you Google “Projectively Extended Real Numbers”.
You mean this one?
Now tell me, do we usually work with the projectively extended real numbers?
One positive infinity doesn’t even necessarily equal another positive infinity, as two expressions might not approach infinity at the same rate. Note the word “approach”. That’s the only way you’re allowed to use infinity/-infinity, by approaching it. It’s not a real number, it doesn’t actually exist. Second, in most contexts (calculus) it strictly refers to magnitude (ie, it can have directionality applied to it). Take a calculus class if you want to learn more.