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Of course. E = MC^2E 0
R = --- = --- = 0
I I
This leads to a contradiction when E=I=0.
Sorta like N/0 - irrelevant nonsense.The circuit wasn't connected. Therefore no measurement was being
made. V = IR has no relevance. R < oo to close the circuit and
for the equation to apply.
It just pops up in mathematic operations. A little puzzling at firstIt can do, but that is not the only reason for sqrt(-1). Its certainly
not how it came about in the first place.
That was my question.Clearly the infinities are
failures of the theory,
Or a failure of the mathematics.
Is there a difference?
The independence of the continuum hypothesis has no apparentSee:
Cohen,P.J., "The Independence of the Continuum Hypothesis." Proc. Nat.
Acad. Sci. U.S.A. 50 1143-148, 1963.
That ZF+GCH |- AC does not imply that ZF+AC |- GCH.Wouldn't that contradict Cohen? I see that ZF + GCH-> CH, and now you
say ZF + GCH -> Axiom of Choice, when Cohen showed /CH + ZFC leads to no
contradiction.
"ZFC+/CH->/CH" is not what you meant to write, surely? Anyway, both CHRight- but ZF + GCH-> AC does mean you now have ZFC, and ZFC+/CH->/CH by
Cohen, so you can't have ZF + GCH-> CH any more.
"Fairly easy" seems to me an exaggeration. Sierpinski's proof is far...but it's fairly
easy to see that ZF + GCH -> AC, since ZF + GCH implies that every
cardinal is an aleph,
But isn't c = 2^aleph-null, and aleph-1 is possibly less than c?Nicholas O. Lindan wrote:
But the size of the set of real numbers is Aleph 1 (oo^2).
Aleph-1 is at least aleph-null^aleph-null.
Seaman's statement "every set can be well ordered" naturally usesI don't think you mean well-ordered in the algebraic sense- you mean a
total ordering on the cardinals.
inevitable babble that arises where discourse contains terms that haveFred Bloggs <nospam@nospam.com> writes:
... because the non-existence of infinity strictly between countability
and first uncountability ( power set of countability) has been shown to
be equivalent to the Axiom of Choice.
You're mistaken about this. Why these ill-informed exchanges in all
these unrelated groups?
Torkel, as Francis Bacon observed hundreds of years ago, this is the
Humm... off hand remark of about the right date, you say, Well it'swas based on an off hand remark by Halmos in his General
Topology, and he was almost certainly referring to this result, the date
is about right.
Ah, the killer unwarranted assumption. Very dangerous.I am assuming that that
snip
maybe that's where I'm going wrong.
And a casual comment intended to add support to an argument or"Fairly easy" seems to me an exaggeration.
Perhaps a question would be more direct than an opinion as to theI don't think you mean well-ordered in the algebraic sense- you mean a
total ordering on the cardinals.
Well... Not _really_, it's just a thought measurement.
---
Careful, you are getting into Planck's range there.
`Two turns' does not necessarily indicate rotation. There is noHow far does an apple roll if it makes two turns?
Exact answer in apple diameters, please.
Androcles
Ambiguous. An apple may turn without rolling at all.
useful abstract concept.isn't a number but we still mix it up with numbers.
Of course it is a number, thats why we treat it as such.
Ok what it's value then?
.
square root of -1 is the number that yields -1 when squared. Another
Alfy - another ambiguous inquiry. An abstract symbol useful in(Was refering to infinity (oo))
Then you are out of luck. I must confess, I thought the apples inI'm still waiting for a jpeg of quantity sqrt(-1) apples.
I confess my imagination does not stretch this far.