How to visualize an accumulation, adherent point.....
Try an explanation and not a definition.......\

Question

How to visualize an accumulation, adherent point.....
Try an explanation and not a definition.......\

jamesj · Answer

Here are two simple examples.

0 is an accumulation point in the reals of this set: A = { 1/n  |  n nonzero integers }

An adherent point of the interval (0,1) is 0, as is 1.

anonymous · Answer

I saw this example in the book but i dont get it can you give me some example that has some real life insight..

jamesj · Answer

This sort of mathematics doesn't work that way.  

They are both technical definitions and I have to say I think these two examples are pretty straight forward.

You develop your intuition about them not by looking for loose analogies in the "real world", but by looking at these examples and others carefully, and be reading a couple of proofs where these definitions are used.

jamesj · Answer

*and BY reading...

anonymous · Answer

Thanks man now i can find some courage to face it

jamesj · Answer

it's not always obvious where these sorts of technical definitions come from or why they'd be useful.  That's why looking at proofs is important.  

I have to say accumulation points come up quite a bit in elementary analysis.  Adherent points is not a concept that's not very useful in my experience.