/sci/ - Science & Math

>>5671217
ah yes... but what digits will it have :D

>>5671191
i wholeheartedly and unwittingly agree with this

>>5671293
>>5671235
nice one

so he didn't say "bigger" he said "greater"
thank you >>5671293 i needed that

>>5671281
i.e. the reference frame is not you, not the room.. not even space.. it is the fabric of space

however.. jump into a fast orbit (around a black hole, just outside the event horizon).. your 3D momentum will change wildly.. but you won't feel a thing because it is the curvature of space itself that's causing the change in your momentum

if portals work through curving the space so that entry and exit align.. no sensory effect would occur, yet the (3D) momentum would do a 180

for it to happen as instantaneously as in te game you would have to go through the hole itself.. which to you would seem to take an infinity and you would die

>>5671266
imagine if you are the only object in the universe an you we're spinning around your axes (like a ballerina)
even though you are standing still relative to yourself.. you will feel your arms being pulled out as they resist change of momentum

>>5670227
good post.. bad english

>>5670846
yea i got that

as i said it can be bijected by the function in >>5670787

but that raises things to the power of infinity and that (i'm told) goes outside the natural numbers.. so there is no bijection after all and i now understand where my flaw was
(confusing integers, natural numbers and ordinals)

>>5670819
i am not an anything major
or i obviously wouldn't be asking questions here
and
> Phrase things intelligently
what fun would that be.. and how would i kill 3 hours of my time otherwise :D

>>5670778
and i guess that that's the lesson i learned today

( lim(x) x-> inf ) =\= ( inf )

> just sure looks like it

thank you /sci/

>>5670760
>>5670755
>>5670750
no.. i can see already that it will end up in the same muck as before

but let me try nevertheless

so what you're saying is that no function exists that can map all real numbers to all natural numbers

how about N = R*10^n where n is the number of digits in R

.. and ok i get it i can't raise to the power of infinity.. just tend towards it as a lim

>>5670750
yes, yes.. now we're getting somewhere

>>5670715
i would guess that the answer to that one is YES

or more verbosely
infinity is always equally far away.. infinitely far away
so it doesn't matter if you count by adding by 1, adding by 10, multiplying by 10 or raising to the power of 10 it will take you the same number of steps to get there
> infinitely many
so if n+1 counts from 1 to inf
then n*10 counts 1 to infinitely many digits
and both of those sets should be equally countable by cantor's definition

and any set with infinitely many digits as a limit is uncountable by cantor's diagonal

makes more sense now? (my numeropathy if nothing else)

>>5670671
>>5670679

i do think that this is a good definition
> in part because
i do believe it agrees with what my problem with cantor's diagonal is:

.. integers are an infinite set: therefore not (1)
.. integers are (2)
.. (2) fails the diagonal test at least as badly as Real numbers
-> therefore integers are an uncountable infinite set
> and cantor's diagonal proof is null and void

NOOO, what did i do wrong now... :D

>>5670671
>>5670679

digesting.. this looks good

not sure if it agrees with me, or explains why i'm wrong

>>5670640
NOOO.. noo.. pls

running that algorithm for an infinite amount of time would SURELY generate numbers of infinite length..

or i seriously misunderstand what infinity is :D

>>5670608
a actually agree and because of
>>5670616
and that is the same answer that satisfies
>>5670628

and that i guess is the core of the issue

there seems to be a number N which is finite but tends to infinity
and my brain is too small to see how that number differs from infinity.

>>5670602
oh... really?.. well yes.. that would bury that
pretty effectively

but i am however hung up on it

how can you have a finite number of digits describing an infinite set of integers

if you can take any integer and multiply it by 10 and get an integer in an infinite set you could repeat the process to infinity

hence my insistance that integers must include numbers with infinite digits

> and there i go beating that again.. sorry...
> and thanks for the discussion

>>5670562
>>5670570
>>5670571
>>5670583
>>5670591

see
>>5670445

you can have any number of zeroes before an integer

as in
1 = 01 = 001 = 0001 etc.
the dots aren't omitted, they're really not there :D
the strange notation is just so that the numbers would fit into cantor's diagonal matrix

>>5670547
is it necessary to go into all that?
i am very much trying to keep integers as a baseline (wherein, perhaps, my fault lies)

so once more (on to the breach)
1. are integers an infinite set? (yes)
2. can you have an infinite set of integers by limiting the number of digits each integer has? (no ? i don't see how)

so if there are integers with infinitely many digits
> hm... all equaling infinity :D now, that might be my problem, but inf+inf=inf so that's ok (i said might)
then there is a 1:1 relation between real numbers and integers
> pi has an integer counterpart in pi*10^înf (well ^inf-1 but it's all the same thing)

so.. ether
1. real numbers are countable,
2. integers are uncountable or
3. integers aren't an infinite set

>>5670546
you could
and it would be a finite set
and would therefore be irrelevant to the discussion
and i am being trolled

>>5670540
i am not proud of that post

>>5670526
> you can have an infinite number of sets each containing a finite number of digits
and that is not what i asked

can you have (ONE) infinite set, of (INFINITELY MANY) numbers where there is a finite limit to the number of digits each number can have

it's a science making yourself clear :D

>>5670493
and we're running around in tighter and tighter circles around the thing that's seems to be the disagreeing question

can you have an infinite set of numbers with a finite limit of digits

>>5670487
if a number of digits is finite, isn't the set then finite as well?

and if normals are a finite set, then why bring them up...

if they are, however, not.. then how can you have an infinite set with finite maximum number of digits