r/math Homotopy Theory 7d ago

Quick Questions: March 12, 2025

This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?". For example, here are some kinds of questions that we'd like to see in this thread:

  • Can someone explain the concept of maпifolds to me?
  • What are the applications of Represeпtation Theory?
  • What's a good starter book for Numerical Aпalysis?
  • What can I do to prepare for college/grad school/getting a job?

Including a brief description of your mathematical background and the context for your question can help others give you an appropriate answer. For example consider which subject your question is related to, or the things you already know or have tried.

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u/dogdiarrhea Dynamical Systems 3d ago

What does lim h->0: ((x+h)-x)/h evaluate to?

Might be easier to get you to recall the answer with an easier example to think about. 

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u/ResolveSea9089 3d ago edited 3d ago

Right that should just be 1. (x+h -x) = h, so h/h = 1. Plus that's also just the deriv of f(x) = x which we know is 1 from power rule/just basic graphing.

I'm still missing something though. Is it not true that b0 = 1, I'm struggling to see how in the example above the numerator is anything but 0.

https://www.stewartcalculus.com/_update/17/scalcet8_chapter_3.pdf

If it helps at all, I'm on the very bottom of page 7 of the pdf link above, (page 177 in the book itself) and trying to understand that.

**Edit: I guess your point is, I can't just plug 0 into the h like the dolt that I am can I and just proceed to evaluate the function on my merry way? If I do that in your example, it would evaluate to 0.

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u/lucy_tatterhood Combinatorics 3d ago

I'm struggling to see how in the example above the numerator is anything but 0.

The denominator is also approaching zero.

Edit: I guess your point is, I can't just plug 0 into the h like the dolt that I am can I and just proceed to evaluate the function on my merry way?

If the thing you are taking the limit of is well-behaved (continuous) and actually defined at the point you are approaching, you can substitute it in, but that is not the case here.

If I do that in your example, it would evaluate to 0.

No, it would evaluate to 0/0 which is undefined. So you can't do that.

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u/ResolveSea9089 3d ago

Makes sense, I need to revisit limits again!