| Science Forum Index » Logic Forum » Fastest Known Algorithm for Decimal Digits of Various... |
|
Page 1 of 1 |
|
| Author |
Message |
| Charlie-Boo... |
 Posted: Sat Oct 31, 2009 4:14 am |
|
|
|
Guest
|
Besides defining fastest and the types of real numbers there are known
to exist (perhaps defining each with a computer program to generate
the numbers of that type) what are the fastest known algorithms for
generating the decimal or binary digits/bits of pi? e? square root of
2? sum of these? pi to the pi power? Could it be that pi to the pi
is equal to 32? What are math's shortest theorems?
But actually in CBL many really big theorems are extremely short in
representation and proof.
C-B |
|
|
| Back to top |
|
|
|
| Mensanator... |
| Posted: Sat Oct 31, 2009 4:58 am |
|
|
|
Guest
|
On Oct 31, 9:14�am, Charlie-Boo <shymath... at (no spam) gmail.com> wrote:
[quote]Besides defining fastest and the types of real numbers there are known
to exist (perhaps defining each with a computer program to generate
the numbers of that type) what are the fastest known algorithms for
generating the decimal or binary digits/bits of pi? �e? square root of
2? �sum of these? �pi to the pi power? �Could it be that pi to the pi
is equal to 32?
[/quote]
Trivially false.
[quote]pii()
3.0 27.0[/quote]
3.1 33.3596319789
3.14 36.3378388802
3.141 36.4158446957
3.1415 36.4549147287
3.14159 36.4619520932
3.141592 36.4621084956
3.1415926 36.4621554164
[quote]�What are math's shortest theorems?
But actually in CBL many really big theorems are extremely short in
representation and proof.
C-B[/quote] |
|
|
| Back to top |
|
|
|
| Charlie-Boo... |
| Posted: Sat Oct 31, 2009 8:37 am |
|
|
|
Guest
|
On Oct 31, 10:58 am, Mensanator <mensana... at (no spam) aol.com> wrote:
[quote]On Oct 31, 9:14 am, Charlie-Boo <shymath... at (no spam) gmail.com> wrote:
Besides defining fastest and the types of real numbers there are known
to exist (perhaps defining each with a computer program to generate
the numbers of that type) what are the fastest known algorithms for
generating the decimal or binary digits/bits of pi? e? square root of
2? sum of these? pi to the pi power? Could it be that pi to the pi
is equal to 32?
Trivially false.
[/quote]
And in general? Prove it is . . . irrational / transcendental
And the types of numbers?
[quote]pii()
3.0 27.0
3.1 33.3596319789
3.14 36.3378388802
3.141 36.4158446957
3.1415 36.4549147287
3.14159 36.4619520932
3.141592 36.4621084956
3.1415926 36.4621554164
What are math's shortest theorems?
But actually in CBL many really big theorems are extremely short in
representation and proof.
C-B- Hide quoted text -
- Show quoted text -[/quote] |
|
|
| Back to top |
|
|
|
| Charlie-Boo... |
| Posted: Sat Oct 31, 2009 8:47 am |
|
|
|
Guest
|
On Oct 31, 11:39 am, Frederick Williams
<frederick.willia... at (no spam) tesco.net> wrote:
[quote]Charlie-Boo wrote:
What are math's shortest theorems?
Its axioms. Assuming that it has some.
[/quote]
Why do you think that? That's not true.
C-B
[quote]--
Which of the seven heavens / Was responsible her smile /
Wouldn't be sure but attested / That, whoever it was, a god /
Worth kneeling-to for a while / Had tabernacled and rested.[/quote] |
|
|
| Back to top |
|
|
|
| Frederick Williams... |
| Posted: Sat Oct 31, 2009 9:39 am |
|
|
|
Guest
|
Charlie-Boo wrote:
[quote]
What are math's shortest theorems?
[/quote]
Its axioms. Assuming that it has some.
--
Which of the seven heavens / Was responsible her smile /
Wouldn't be sure but attested / That, whoever it was, a god /
Worth kneeling-to for a while / Had tabernacled and rested. |
|
|
| Back to top |
|
|
|
| jbriggs444... |
| Posted: Mon Nov 02, 2009 3:27 am |
|
|
|
Guest
|
On Nov 2, 4:28 am, Frederick Williams <frederick.willia... at (no spam) tesco.net>
wrote:
[quote]Charlie-Boo wrote:
On Oct 31, 11:39 am, Frederick Williams
frederick.willia... at (no spam) tesco.net> wrote:
Charlie-Boo wrote:
What are math's shortest theorems?
Its axioms. Assuming that it has some.
Why do you think that? That's not true.
Well, if x = x were an axiom it would also be a pretty short theorem.
The point of my 'assuming that it has some' was that it is not clear to
me what the axioms of mathematics--in it's generality--are.
[/quote]
Caveat: all I know about first order logic is what I picked up lurking
here.
[Many systems of] mathematics can be understood in the context of
first order logic with equality.
http://en.wikipedia.org/wiki/First-order_logic#Equality_and_its_axioms
You get the axiom (or axiom schema) that asserts: "Ax x=x" from that
source.
Personally, I'd rather see the theorem stated as "1=1" or "Ax x=x"
rather than "x=x". The latter looks like a predicate with one free
variable. Theorems should not contain free variables. Instantiate
them away or bind them up. |
|
|
| Back to top |
|
|
|
| Frederick Williams... |
| Posted: Mon Nov 02, 2009 4:28 am |
|
|
|
Guest
|
Charlie-Boo wrote:
[quote]
On Oct 31, 11:39 am, Frederick Williams
frederick.willia... at (no spam) tesco.net> wrote:
Charlie-Boo wrote:
What are math's shortest theorems?
Its axioms. Assuming that it has some.
Why do you think that? That's not true.
[/quote]
Well, if x = x were an axiom it would also be a pretty short theorem.
The point of my 'assuming that it has some' was that it is not clear to
me what the axioms of mathematics--in it's generality--are.
--
Which of the seven heavens / Was responsible her smile /
Wouldn't be sure but attested / That, whoever it was, a god /
Worth kneeling-to for a while / Had tabernacled and rested. |
|
|
| Back to top |
|
|
|
|
