Need help on some problems w/ accumulation points

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Homework Statement


Give an example of a set with exactly two accumulation points.



Homework Equations


We can use the defintion of accumulation points

The Attempt at a Solution



I really have no idea where to get started on this. If I could get a hint that would be great thank you
 
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Well, you listed the "definition of accumulation points" as a "relevant equation"! What is that definition.

Suppose you had a sequence such as {1, 1/2, 1/3, ..., 1/n, ...}. That is a set of real numbers. What are its accumulation points?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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