Re: Line does not consist of points..

On Apr 7, 4:54 pm, amy666 <tommy1...@xxxxxxxxxxx>
wrote:
david wrote :





On Sun, 06 Apr 2008 16:43:18 EDT, amy666
<tommy1...@xxxxxxxxxxx>
wrote:

jonas wrote :

On 5 Apr, 03:42, "mina_world"
<mina_wo...@xxxxxxxxxxx> wrote:
Hello teacher~

If line consists of points,  the length of
line
is
0.
So, line does not consist of points.

How do you think about it ?

Well if lengths 0 there is no line, if there
is
zero
apples there is
no apples. I think that pretty much wrap the
whole
thing up, a line of
0 length is only a numerical value put to an
object
that does not
exist.

but perhaps a line is made up of points.

points have length " 0 " but only as a limit.

N0, the length of the set {a} is 0, period.
Nothing
to do with limits.

a point might have a kind of infinitesimal
length
"h".

Perhaps pigs have wings. In _fact_ a point does
_not_
have an infinitesmal length h (unless you mean h
= 0,
which of course you don't).

as lwalke , venkat and others ( like archimedus
plutonium, mina , ... if im not mistaken ) ( and
me )
have considered the inverse of cardinal size , so
that

"h" * cardin. of a line [0,1] = 1 (length)

This doesn't work. Say c is the cardinality of
[0,1].
Then c is _also_ the cardinality of [0,2]. So if
what you're saying is going to work we must have

h * c = 1

and _also_

h * c = 2.

Hence 1 = 2.

c = 2c

h*c = 1

h*2c = 2

1 = 2  in the sence that a line [0,1] has the same
amount of points as [0,2].

the paradox is caused by your "c" not by my "h".

to show this =>

c = 2c

( c =/= 0 => divide both by c )

1 = 2.

but since there is a point to point mapping from
[0,1] -> [0,2] or vice versa , its not even a real
paradox.

if we map [0,2] to [0,1] before we measure the
length we have indeed 1 = 2.

its just set theory in full glory.

so you made no mistake.

but neither did i.







or similar stuff.

*****

assume a line is not made up out of points ,
then a
line is made up out of .... ??

since every number on a line can be considered a
point, (naive ?) logic implies

1) every set of numbers maps 1 to 1 to points.

2) (real) line is made up out of (real) numbers.

3) line is made up out of points.

if not , then what is a line made of ?

answering : even smaller pieces of lines.

is just selfreference and avoids the question.

regards

tommy1729

David C. Ullrich

regards
tommy1729- Hide quoted text -

- Show quoted text -- Hide quoted text -

- Show quoted text -

obviously, ullrich doesn't understand what
anti-cantorians clearly cee

becuase he is limited to his "line" and "set"
definitions, and cannot
understand how u can both be correct

nver the less, lajofl vioal qui sone limit deq ljvme!

kniishes

amy


no.

david is not wrong here.

altough he does not seem to fully understand my argument , he is not wrong.

if h exists than devision by c needs to be accepted since 1/c = h.

instead of working with numbers i should perhaps stick with cardinals.

to avoid stuff like h*c = 1 = 2.

h*c = finite.

this is more logical.

however c^2 = c.

thus h*(c*c) = h*c = finite

but (h*c)*c = finite*c = c.

a contradiction.

in standard set theory this is solved by not allowing divisions by c or other cardinals, saying they are "undefined" or " forbidden".

and thats no lie.

giving up commutativ multiplication is not my style.

( in fact i dont consider non-commutativ algebra valid, unless for matrices (which i dont consider as a number but a set of variables or equations ) despite of course most numbers have matrix representations )

perhaps we should also forbid c^2 too.
( in this context , not entire set theory of course )

since the relation c^2 = c
is also 1/c.

david himself agreed there is no problem with line only exists out of points.

and neither with an uncountable sum.

and an uncountable sum of 0's = 0.

yet he does not seem the analogue then with a point has length 0 , line has uncountable points (and nothing else but points !), line has lenght 0.

regards to david.

not to fake amys tommys or whoever you also claim to be.

tommy1729
.

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