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Science
In reply to the discussion: If you're having math problems, I feel bad for you, son... [View all]Joseph8th
(228 posts)28. But then pi's special in its relationship...
... with e, too!
Euler's Identity (I know, he had lots of things named after him ... fame and glory, baby) tell us if we're working with complex numbers (x,y) in RxR, with handy notation x + i*y = z is a complex number in C (the field of complex #s), where i = sqrt(-1) is the imaginary number, that we can derive beautiful results from the utterly beguiling equation:
e^{i*pi} + 1 = 0
Wikipedia (started by mathematicians) puts it nicely:
Euler's identity is considered by many to be remarkable for its mathematical beauty. These three basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants:
The number 0, the additive identity.
The number 1, the multiplicative identity.
The number π, which is ubiquitous in trigonometry, the geometry of Euclidean space, and analytical mathematics (π = 3.14159265...)
The number e, the base of natural logarithms, which occurs widely in mathematical and scientific analysis (e = 2.718281828...). Both π and e are transcendental numbers.
The number i, the imaginary unit of the complex numbers, a field of numbers that contains the roots of all polynomials (that are not constants), and whose study leads to deeper insights into many areas of algebra and calculus, such as integration in calculus.
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Question for math teacher - Please. At the end of the year I have 100,000 Pesos...
wake.up.america
Feb 2013
#43
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
As simply as it can be put, your statement is in direct contradiction to a Zermelo-Fraenkel axiom.
Jim__
Mar 2012
#12
Yeah, it guarantees the size N is infinite, not that any number in N is infinite.
napoleon_in_rags
Apr 2012
#20
I'm just incredibly glad to hear these people seeing the holes in set theory.
napoleon_in_rags
Apr 2012
#39