Your perspective of "set theory" is not the normal math perspective. If it works for you, fine — jgill
I'm also curious why you just skipped over the whole part about a vecor being defined by element association since that was the mathematics perspective and the practical application perspective. — SkyLeach
Yes, it's literally the first sentence.In mathematics and physics, a vector is an element of a vector space.
In mathematics, physics, and engineering, a vector space (also called a linear space) is a set of objects called vectors, which may be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but some vector spaces have scalar multiplication by complex numbers or, generally, by a scalar from any mathematic field.
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do.
{(5, 2, 4, 0, 0.0), (5, 2, 4, 1, 0.8414709848078965), (5, 2, 4, 2, 0.9092974268256817), (5, 2, 4, 3, 0.1411200080598672), (5, 2, 4, 4, -0.7568024953079282), (5, 2, 4, 5, -0.9589242746631385), (5, 2, 4, 6, -0.27941549819892586), (5, 2, 4, 7, 0.6569865987187891), (5, 2, 4, 8, 0.9893582466233818), (5, 2, 4, 9, 0.4121184852417566), (5, 2, 4, 10, -0.5440211108893698), (5, 2, 4, 11, -0.9999902065507035), (5, 2, 4, 12, -0.5365729180004349), (5, 2, 4, 13, 0.4201670368266409), (5, 2, 4, 14, 0.9906073556948704), (5, 2, 4, 15, 0.6502878401571168), (5, 2, 4, 16, -0.2879033166650653), (5, 2, 4, 17, -0.9613974918795568), (5, 2, 4, 18, -0.7509872467716762), (5, 2, 4, 19, 0.14987720966295234)}
Are you arguing this way?:
The set of real numbers can't be counted.
Consciousness can't be counted.
Consciousness is not mathematical.
Therefore, the set of real numbers is not mathematical. — TonesInDeepFreeze
AFAIK one doesn't use braces for subsets — SkyLeach
This is not just a matter of notation, but is a crucial concept, especially in linear algebra — TonesInDeepFreeze
AFAIK one doesn't use braces for subsets but then since I'm not a mathematician by trade I don't really know anything about how mathematicians do things — SkyLeach
I don't know why someone would be posting such bold claims as yours about mathematics and linear algebra while not even knowing that there is a distinction between merely a set and an ordered tuple.
Saying that linear algebra is the foundation of mathematics while not knowing the basic notion of an ordered tuple is like saying benzene rings are the foundation of chemistry while not knowing what an atom is. — TonesInDeepFreeze
angry people — SkyLeach
you're literally talking about writing style — SkyLeach
It's not a joke, he's saying that your semantic mess is ridiculous. — SkyLeach
Once again, my colleague Stephen Hawking has upset the apple cart. The event horizon surrounding a black hole was once though to be an imaginary sphere. But recent theories indicate that it may actually be physical, maybe even a sphere of fire. But I don't trust any of these calculations until we have a full-blown string theory calculation, since Einstein's theory by itself is incomplete. — Michio Kaku
Combining quantum entanglement with wormholes yields mind boggling results about black holes. But I don't trust them until we have a theory of everything which can combine quantum effects with general relativity. i.e. we need to have a full blown string theory resolve this sticky question. — Michio Kaku
If ∞ does that to math, is ∞ mathematical? — Agent Smith
If ∞ does that to math, is ∞ mathematical?
— Agent Smith
Nope. It doesn't do that. That's a linear assumption, NOT an axiom. It's not a proof. It isn't part of mathematics at all. It's just a belief held by some people with big egos and funding to defend. — SkyLeach
\sqrt(\infinity*\infinity)=\infinity*1
∞+1= ∞+1-1= ∞*1
f(x)=∑n=−∞∞cne2πi(n/T)x=∑n=−∞∞f^(ξn)e2πiξnxΔξ
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