Is pi Infinite 2

1. Mar 15, 2004

pallidin

Thanks, everyone for the original postings.

Question: If a diameter of 1 ascribes a circle of pi, does it it not lead to the conclusion that pi is determinate? After all, is this not a properly constrained system?

2. Mar 15, 2004

Janitor

HEY!

We've done pi to death. Why don't we ask if e is infinite?

3. Mar 16, 2004

Integral

Staff Emeritus
Or $$\sqrt 2$$

4. Mar 16, 2004

Just for good measure, how about $\pi e \sqrt{2}$?

5. Mar 16, 2004

matt grime

But are you sure you've drawn a diameter of exactly one inch? Might it not be .9999999999999999 inches? YOu sure? How are you going to check? And when did infinite start to mean indeterminate, and in what sense are you using that word?

6. Mar 16, 2004

HallsofIvy

Quite frankly, what does this mean? "If a diameter of ascribes a circle of pi". I confess I don't know the word "ascribes" and I don't know what "a circle of pi" could mean.

In any case, "does it not lead to a conclusion that pi is determinate?" puzzles me. What do you mean by "determinate". pi is, of course, a perfectly we determined number. We know exactly what pi is.

7. Mar 16, 2004

Michael D. Sewell

Enough pi! pi can be described and defined in a very short paragraph, that's all the attention that it deserves.

8. Mar 16, 2004

pallidin

OK, point taken! Sorry for beating a dead horse.

Issue is now closed!

9. Mar 17, 2004

Organic

There is no limit to a content of a set if it can be compared with N members, therefore set b, which is the binary representation of Pi, is a legal set:

Code (Text):

[b][i]b[/i][/b] = {'1_1','1_2','1_3','1_4','0_1','0_2',...}
[b][i]N[/i][/b] = {  1 ,   2 ,   3 ,   4 ,   5 ,   6 ,...}

No chroot, please clrealy show why b is not a legal set.

Also please explain why circle's perimeter/diameter(=Pi) representations are ignored by Standard Math?

Last edited: Mar 17, 2004
10. Mar 17, 2004

matt grime

Chroot was making the point that you never acknowledge. Namely that things are only equal when they are equal. The set (b_n) n in N of the elements of the decimal expansion of pi is NOT equal to pi, nor is it equal to the SET of rational approximations.

A set is a set is a set.

Where does chroot say anthing about legality of sets or otherwise?

But then you're happy to equate the empty set and an inequality, so why should we expect you to follow basic conventions and definitions? Just try and remember when other people write things using mathematical terms they are (in all probability) using them in the proper sense, not in whatever way you happen to think it might be.

11. Mar 17, 2004

Organic

By Standard Math Pi is one of infinitely many irrational numbers of the real line.

Pi is interesting because it is the result of the circle's perimeter/diameter, which is the most symmetrical geometric form, and symmetry is maybe one of the most important concepts of Math language.

Standard Math ignores the verity of structural representation possibilities of Pi and taking care only to its quantitative value that determinates its exact place in the real line.

So I am asking again, please explain why circle's perimeter/diameter(=Pi) representations are ignored by Standard Math?

Last edited: Mar 17, 2004
12. Mar 17, 2004

Hurkyl

Staff Emeritus
Because the "structural representation possibilities" (whatever those may be) are irrelevant when one is concerned with the value.

13. Mar 17, 2004

Organic

Then why structural representation possibilities are not valueable to Standard Math?

14. Mar 17, 2004

Hurkyl

Staff Emeritus
*dun-dun* *tcssshhh*

Bah, where is a drumset smiley when you need it?

15. Mar 18, 2004

KingNothing

I agree. Things like prime numbers or perfect numbers could have much more extensive discussions on them.

16. Mar 19, 2004

Bob3141592

So what's wrong with pi?

Now, if I can only get an infinitely long screen name....

17. Mar 20, 2004

Michael D. Sewell

Nothing. After all these years it hasn't failed me yet.
-Mike