Two young mathematicians investigate the arithmetic of large and small numbers.
- Devyn
- Hey Riley, I’m having a little trouble with this limit
- Riley
- Well, just plug in and see what you get, right?
- Devyn
- I tried that, here’s what I got...
- Riley
- Hm, so that... equals 1 right? I mean, anything divided by itself must be 1?
- Devyn
- I was thinking the same thing. Initially. But then I tried simplifying stuff first and look what happened.
- Riley
- Ok... so the answer is 4? Or is it 1? It can’t be both right?
- Devyn
- Right, that’s why I’m stuck.
- Riley
- Well, we originally thought it was 1 because it was “a number divided by itself.” But that number was zero, and dividing by zero is usually where things go wrong in math.
- Devyn
- Good point. Come to think of it, I can’t just plug in the limit value because that only works when the function is continuous at that point. And I can’t evaluate the top and bottom separately like that, because that limit law only works when the bottom isn’t zero. Crap, I really messed that one up, the limit must be then. Thanks!
- Devyn
- ...
- Devyn
- Also, uh, don’t mention this conversation to anybody ok?
- Riley
- What conversation?
- Devyn
- Exactly.
Consider the function
Consider the function
Consider the function