Thread: topology ans sequences

Can you find any sequence of rationals such that it converges to π/4?

use the fact that the rationals are dense in the reals,
or you can think about the decimal expansion of π/4. How can you get rational numbers out of that, rational numbers that converge to π/4?

Can anybody help me with this immediately??

use the fact that the rationals are dense in the reals to find the answer for this,,,

Let f:R→R be a continuous function such that f(q)=sinq for q∈Q (rational numbers). Find the value of f(π/4).

Originally Posted by chath

...
or you can think about the decimal expansion of π/4

If the question was just asking about , I'd suggest this rational sequence to you:





Etc.

no not about pi.i need a rational function that converges to pi/4

I have this idea...to find f(π/4) we need to pick a sequence xn→π/4 and investigate what f(xn) converges to....will that be ok for this???

Originally Posted by chath

no not about pi.i need a rational function that converges to pi/4

The example I gave was meant to be suggestive of how you could construct a rational sequence for

Think about it a minute. Each of those, each term in the sequence, is rational, and their limit goes to .

So can you think of a different-but-related sequence of rationals whose limit goes to

Originally Posted by chath

I have this idea...to find f(π/4) we need to pick a sequence xn→π/4 and investigate what f(xn) converges to....will that be ok for this???

it sounds like you're thinking along these lines:

Find a sequence converging to , and then will converge to

If so, that isn't going to get you very far, because there's a complication with the function not having an inverse (though, by restricting domains, that can be delt with), and, vastly more intractable, you're going to need these to be rational.