Strange questions regarding infinity

[Steven G]

I am surprised that I did not think of this before.

We know that there are many infinities, this is a given.

Now when we say a limit = infinity or a series goes to infinity then it is reasonable to think which infinity it goes to.

I thought about this for a bit but am getting nowhere with it.

Can someone enlighten me please?

Thanks!

 

[Romsek]

You're going to need to specify the context in which you are taking a limit.

 

[Steven G]

Very interesting!

Can you tell me why these results you stated above are true?

 

[Romsek]

results?

 

[Dr.Peterson]

I am surprised that I did not think of this before.

We know that there are many infinities, this is a given.

Now when we say a limit = infinity or a series goes to infinity then it is reasonable to think which infinity it goes to.

When we say a limit is infinity, we are not saying that it equals a number called infinity! It is just a euphemism, you might say, for "increases without bound". Assuming the context is real-valued functions, "infinity" is not an element of the set of real numbers. Infinite limits have a different definition than finite limits, because we can't subtract infinity from a real number, for example.

And if we extend the real numbers with +infinity and -infinity, that is not one of the "infinities" studied in set theory. It is a different category.

So your question is ultimately meaningless.

 

[Steven G]

When we say a limit is infinity, we are not saying that it equals a number called infinity! It is just a euphemism, you might say, for "increases without bound". Assuming the context is real-valued functions, "infinity" is not an element of the set of real numbers. Infinite limits have a different definition than finite limits, because we can't subtract infinity from a real number, for example.

And if we extend the real numbers with +infinity and -infinity, that is not one of the "infinities" studied in set theory. It is a different category.

So your question is ultimately meaningless.

OK, I see what you are saying. I just have to let what you say settle in. Thanks.