blackpenredpen

math for fun 

To see this working, head to your live site.
  • Categories
  • All Posts
  • My Posts
BP31 (BluePi31415)
Feb 09, 2019

inf*inf

in Math Problems

I understand that when you have a limit with a product going to 0*inf, you cannot determine the limit yet, but what about when the product goes to inf*inf? Are we allowed to say that that is infinity, or is it still indeterminate like 0*inf? Thank you!

3 comments
0
ahaar13
Feb 09, 2019

It's just infinity. Think of like lim as x goes to inf of x^2. That's just like the lim of x*x, which is inf*inf. Or you could just think huge number times huge number is also huge; likewise inf*inf is inf (an even larger infinity, even).

0
BP31 (BluePi31415)
Feb 09, 2019

That was my initial idea as well, but can it be proven? My teacher said that we can not just assume that.

0
ahaar13
Feb 09, 2019

Well, you could do an epsilon-delta proof if you're in an analysis class, but if you're taking like calc 1, 2, or 3 then you can definitely assume inf*inf goes to inf. I mean, for a bit of an explanation, inf*(anything)=inf as long as the anything is not 0 (sure, we can do negatives and make it -inf, but same idea). Furthermore, inf is not 0, it's not even a number, so inf*inf must be inf.

0
3 comments