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. ...
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.
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.