Science

tama

(9,137 posts)

6. Transcendentals are strange

Mon Mar 26, 2012, 09:34 AM

Mar 2012

AFAIK, being not an algebraic number is other way of saying 'not constructible with compass and ruler (circles and lines). Very few transcendentals are known to be such and proving them are hard problems of math, yet it is known(?) that the points of real line consist mainly of transcendentals. So there is a relation between the notion of infinitesimals and transcendentals to make the real line smooth and continuous.

From a more general view transcendental pi is known to be transcendental because as a mathematical constant it is in some sense the irreducible ratio of compass and ruler, and because it has been proven (at least inside the axioms of standard set theory) that a circle can't be squared.

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If you're having math problems, I feel bad for you, son... [View all] tridim Mar 2012 OP

R&K for the first math post I've seen on DU longship Mar 2012 #1

Question for math teacher - Please. At the end of the year I have 100,000 Pesos... wake.up.america Feb 2013 #43

Well, it doesn't come out even. longship Feb 2013 #44

I disagree. Is PI a rational number? napoleon_in_rags Mar 2012 #2

Woot! for critical thinking and logic! TalkingDog Mar 2012 #3

A set of numbers is countable if it has the same cardinality as some subset of the natural numbers. Jim__ Mar 2012 #4

"there do not exist 2 integers, say n and m, such that pi can be written as n/m" napoleon_in_rags Mar 2012 #5

"... you know Z plus all integers of infinite length would probably have the same cardinality as R." Jim__ Mar 2012 #7

+! Hawkowl Mar 2012 #8

I will make it simpler for you. napoleon_in_rags Mar 2012 #9

"God created the integers" one_true_leroy Mar 2012 #10

This is a teachable moment. napoleon_in_rags Mar 2012 #11

A few points... one_true_leroy Mar 2012 #13

Yes, I've always had something of a flirtation with limits... napoleon_in_rags Mar 2012 #15

Had to jump in on this thread... Joseph8th Apr 2012 #22

As simply as it can be put, your statement is in direct contradiction to a Zermelo-Fraenkel axiom. Jim__ Mar 2012 #12

Awwwww hell..... one_true_leroy Mar 2012 #14

HELL yeah! I love it... Joseph8th Apr 2012 #23

Ah, my friend. You have forgotten your transfinite cardinals! napoleon_in_rags Mar 2012 #16

Guess again. Jim__ Mar 2012 #17

So you're saying 1+1+1...infinity is an integer? napoleon_in_rags Mar 2012 #18

The Axiom of Infinity says that 1 + 1 + 1 + 1 ... is an integer. Jim__ Apr 2012 #19

Yeah, it guarantees the size N is infinite, not that any number in N is infinite. napoleon_in_rags Apr 2012 #20

See post #4. Jim__ Apr 2012 #21

Nicely said... and... Joseph8th Apr 2012 #24

Now there's some interesting stuff. napoleon_in_rags Apr 2012 #26

Wellll.... Joseph8th Apr 2012 #27

But then pi's special in its relationship... Joseph8th Apr 2012 #28

Euler's identity tama Apr 2012 #30

Just answer me one question Joseph8th. napoleon_in_rags Apr 2012 #32

You're on an interesting track tama Apr 2012 #33

You're awesome Tama. napoleon_in_rags Apr 2012 #34

Mersenne primes tama Apr 2012 #35

God is Alive, Magic is Afoot. napoleon_in_rags Apr 2012 #36

Category theory tama Apr 2012 #37

I'm just incredibly glad to hear these people seeing the holes in set theory. napoleon_in_rags Apr 2012 #39

Not quite. Dr. Strange Apr 2012 #38

.999... is not equal to 1. napoleon_in_rags Apr 2012 #40

The problem is you can't treat infinity like a real number. Dr. Strange Apr 2012 #41

Agreed, that is the problem, but for both of us. napoleon_in_rags Apr 2012 #42

Not much point tama Apr 2012 #31

Transcendentals are strange tama Mar 2012 #6

Da! Transcendentals are strange... Joseph8th Apr 2012 #25

Deep shit ;) tama Apr 2012 #29