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bobbym wrote:

I do lots of analytical geometry, I prefer it to Eucidean. Why not post your questions, that is how you get help on a forum.

What is analytical geometry, again?

And that gave you zeta(3)?

But how did you go about doing it?

Yes, I have a closed form answer

Yep, that lower bound is correct.

How about 8 digits?

That upper bound is correct. How do I do better?

How would an experimental mathematician do it?

**Agnishom**- Replies: 20

How do I approximate the following Triple Sum?

zetafunc wrote:

I spent about 4 years posting as a guest on this forum, before everything updated and forced me to register in order to reply to threads (as it stands, guests are able to create threads, but are not able to reply to them, for whatever reason).

How does it make you feel that you're a member now?

Linelites wrote:

In trying to fully grok the concept of irrational vs. rational, I try to visualize the difference between them represented by two Pythagorean Triangles. One triangle, like the 3,4,5, will have commensurate, rational values between the legs and hypotenuse. Change the aspect slightly, so as to make it 3,1, and the sqrt of 10, and the legs and hypotenuse are now incommensurate and irrationality introduced. My question is: by what mechanism does this occur? Why should a slight shift in aspect of the legs take us from one realm of numbers to another?

I am a hobbyist, this is my first post. Perhaps the answer is obvious, but it eludes me and I hope someone can help me. Perhaps it is purely a numerical property that is detached from the physical representations of geometry and therefore lacks any mechanism.

This should not be posted in Help Me!

Because you're being philosophic here, I'd want to point out to you that the rational numbers are dense in the reals. Or put in a more fancy way, there is a rational between any two irrationals and an irrational between any rationals. So, there is not much work to be done to switch over from rationals to irrationals.

Not really, does it?

You look a little thin, have you been eating?

What are you talking about?

**Agnishom**- Replies: 2

My friend Sneha has this problem

Okay, here is a proof.

Construct a sequence with elements in S such that all terms are different. This should be possible because S is infinite. Now, because this sequence is bounded, it must have a convergent subsequence which is non-constant.

Hence, it follows that S' is non-empty.

Have you seen the proof of the fact that there is a rational number between any two reals?

By S', do you mean the set of all limit points of S?

You are right. I should tell him about online compilers.

No, I didn't miss the rants. Is that even possible?

That code is fine. But the point of my code was to demonstrate an overflow

**Agnishom**- Replies: 7

I once claimed in some forum that the following code in C is an infinite loop:

```
#include <stdio.h>
int main(void) {
char i;
for (i=0; i <256; i++)
printf("%d\n", i);
return 0;
}
```

Somebody wrote:

How is this program an infinite loop? Unless char I doesn't increment because it's a character and not an integer.

I wrote:

Before I go ahead and answer that question, I personally encourage you to actually put this in a compiler and run the code for yourself and check that it indeed is an infinite loop.

Somebody wrote:

I don't have a compiler, but I know enough about coding to know that for loops shouldn't be infinite loops. So if it doesn't output integers, then it must be an error of sort.

What?! How can someone not have a compiler but *know enough about coding*?

But why is the manifold expanding?

What is the Leibniz rule about?

You can post them on Brilliant

Why did you do that? I do not think you ran out of delta waves.

Which problems did you stop posting?