### Limit NO. 1 : The limit points of the sin n sequence

14Nov08

The proof for the limit points of the sequence haven’t given me a calm dream until today.

Of course the limit points of that sequence (almost intuitively)

**Lemma.**

**Lemma proof.**

from floor function definition we have the following inequality:

Now we will prove that

Let where

So we have

Let

so of course

Lets consider

and look closer at

The following is true

It’s also simple to show (for example geometricly), that we can find such that the following inequality is satisfied

Now we will consider

From which

And that means that for all so ■

**Proof.**

We’ll show that

Lets take where and

Then ( because the step is smaller then the range)

So when’ll take then

which satisfies the limit definition. ■

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Filed under: Mathematics, Science | 1 Comment

Tags: limit, points, sequence, sin, sin n, sinn

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Thanks for your Solution and I appreciate you for having a serious fight with this problem as I have spent some days like you.

Cheers