Do You Have a Problem with Infinity?

[Desert Snake]

forever is a long time

even God's Favored failed to hold position in heaven

This is unclear. In other words, I don't know what you mean by this.

 

[joelr]

The continuum hypothesis is NOT the question of whether there is an infinite cardinal between aleph_0 and aleph_1. Since, *by definition*, aleph_1 is the next cardinal after aleph_0, there isn't.

The question is whether the cardinality of the real line is the same as aleph_1. In other words, are there infinite subsets of the reals that cannot be put into one-to-one correspondence with either the set of natural numbers nor the set of real numbers.

And, it turns out, this problem has been solved, in a fashion: it has been shown to be independent of the other axioms of set theory: in other words, it can neither be proved nor disproved from the usual axiom list. So, in a strong sense, it is unsolvable.

Nonetheless, some are trying to find *other* axioms that might be generally accepted (usually a large cardinal axiom) and give a resolution to CH.

Same difference. Except I said between 1 and 2 which was wrong, the first infinity - integers, is Aleph_null and the reals are Aleph_1


the continuum hypothesis says that there is no set

for which ℵ 0 < | S | < 2 ℵ 0 .

(2^ aleph0) is just aleph_1

so it's saying the reals are not greater than aleph0 but smaller than aleph1
So the integers are aleph0 and the reals are aleph1. That there isn't another infinity in between the 2 aleph0/aleph1.

Basically what I was saying.

 

[Thief]

What you're saying doesn't make sense. Light moves at the fastest possible speed yet has zero time in it's reference frame.

Time is a vector, for one.
When you make plans to meet someone you give a spatial location. But you also have to give another location, a time location.
Something in space that has no motion through space will still be moving through the time dimension.

dimensions ARE cognitive devices
length is a measure
height and width ...measure

movement is a division of a length
by another measure......units of time
another cognitive device

tme is not a substance
not a force

miles per hr
vibrations per sec
the movement of light measured by a year

movement is real
and the space between one item and another.....real

the quotient is in your head

 

[Thief]

This is unclear. In other words, I don't know what you mean by this.

a story I grew up with....not sure the source

God gave an instruction and one third of heaven said ......Nay!
God's Favored....Keeper of the Light
led the rebellion

if position at God's right hand can be lost

then NO position is guaranteed

even if both your feet are IN heaven
and you stand beside the Almighty Himself

 

[Polymath257]

Same difference. Except I said between 1 and 2 which was wrong, the first infinity - integers, is Aleph_null and the reals are Aleph_1


the continuum hypothesis says that there is no set

for which ℵ 0 < | S | < 2 ℵ 0 .

I assume you mean 2^aleph_0, not 2 times aleph_0 here.

(2^ aleph0) is just aleph_1

No, whether this is true is the content of the Continuum hypothesis. The cardinal 2^alpeph_0 is the cardinal of the set of real numbers. That is true. But aleph_1 is *defined* to be the next cardinal large than aleph_0. So, by definition, there are no cardinals between them. So the question of the continuum hypothesis is whether 2^aleph_0 = aleph_1.

so it's saying the reals are not greater than aleph0 but smaller than aleph1
So the integers are aleph0 and the reals are aleph1. That there isn't another infinity in between the 2 aleph0/aleph1.

Basically what I was saying.

No, the reals are 2^aleph_0. The whether that is the same as aleph_1.

Or, alternatively, we know 2^aleph_0 is a cardinal. We know that every cardinal is aleph_k for some ordinal number k. The more general question is what the value of k is in this equation. The CH ask, specifically, if k=1.

But, you are correct that the CH is also the question of whether there are any infinite subsets of the reals that are neither the cardinality of the natural numbers or the cardinality of the reals.

I know of one popular book that mistakes 2^aleph_0 and aleph_1. If I recall, it was Gamov's 1,2,3,..infinity. If that is your source, be careful!

/E: This might be helpful: Continuum hypothesis - Wikipedia

In particular, the section on Cardinality of Infinite Sets

 

[joelr]

dimensions ARE cognitive devices
length is a measure
height and width ...measure

movement is a division of a length
by another measure......units of time
another cognitive device

tme is not a substance
not a force

miles per hr
vibrations per sec
the movement of light measured by a year

movement is real
and the space between one item and another.....real

the quotient is in your head

but you're not understanding that time and space are equally as real in physics.
You just said space is real but when travelling near light speed length becomes relative to different observers.
To us the SLAC collider is 26 miles long. To photons at 99.999 light speed it's only 12 feet long.

Same with time, different observers experience different rates of time at different speeds.

When one moves through the space dimension your time movement slows. At max speed through space you travel zero through the time dimension.
These are real constructs. If space is real then the time dimension is just as real.

In fact in a black hole the 2 reverse, space becomes time-like and time becomes space-like. How could this happen if one were just a "mental construct"? It can't. It can because they are real dimensions rather than "mind constructs"
You've been reading too much fiction or some bad pop-science.

 

[Thief]

but you're not understanding that time and space are equally as real in physics.
You just said space is real but when travelling near light speed length becomes relative to different observers.
To us the SLAC collider is 26 miles long. To photons at 99.999 light speed it's only 12 feet long.

Same with time, different observers experience different rates of time at different speeds.

When one moves through the space dimension your time movement slows. At max speed through space you travel zero through the time dimension.
These are real constructs. If space is real then the time dimension is just as real.

In fact in a black hole the 2 reverse, space becomes time-like and time becomes space-like. How could this happen if one were just a "mental construct"? It can't. It can because they are real dimensions rather than "mind constructs"
You've been reading too much fiction or some bad pop-science.

not at all....

time is a measurement
it is not a force or a substance

 

[Polymath257]

not at all....

time is a measurement
it is not a force or a substance

The same can be said about space.

 

[Thief]

The same can be said about space.

nice try.....

space is real enough....

it's all that nothing in between the substance

 

[Polymath257]

nice try.....

space is real enough....

it's all that nothing in between the substance

And time is all that duration between events.

 

[Thief]

And time is all that duration between events.

movement is real

the gage is manmade and cognitive
the measure of distance......man made
the measure of time....man made

a man made measure divided by another man made measure

time is all in your head

 

[Thief]

And time is all that duration between events.

that would be a record
also manmade

now an event might be interesting......

let's see if you can.......see

picture an object self illuminating
and moving toward you at the speed of light

what do you see?

 

[ratiocinator]

time is all in your head

Nonsense. Time and space are combined - there is only space-time. Different observers' time dimensions point in different directions through space-time. You cannot separate them. There is plenty of evidence of this.

 

[Thief]

Nonsense. Time and space are combined - there is only space-time. Different observers' time dimensions point in different directions through space-time. You cannot separate them. There is plenty of evidence of this.

movement will happen.....whether you measure it or not

the measure is not required for reality to happen

 

[joelr]

movement will happen.....whether you measure it or not

the measure is not required for reality to happen

As you accelerate through space your time movement slows down. We measure this with atomic clocks.
At light speed movement through time completely stops. Because time is an actual dimension.

In black holes space and time reverse. Not because time is "in the black holes head" but because just like space, time is a dimension.

Both cases demonstrate that your pop-pseudo-sci ideas about time are not based in reality.

What they are probably based in is the mistaken idea that time is an illusion.
That bro-science came from the fact that it's believed in physics that the "passage" of time is in our minds. But it doesn't say that all time is an illusion. But people got wind of this concept and of course they completely messes up what the concept was actually saying.
It was actually Einstein. And the passage of time, not time itself.

Relativistic effects happen to space (length contraction) and time equally. They are 2 sides to the same coin.

 

[Thief]

As you accelerate through space your time movement slows down. We measure this with atomic clocks.
At light speed movement through time completely stops. Because time is an actual dimension.

In black holes space and time reverse. Not because time is "in the black holes head" but because just like space, time is a dimension.

Both cases demonstrate that your pop-pseudo-sci ideas about time are not based in reality.

What they are probably based in is the mistaken idea that time is an illusion.
That bro-science came from the fact that it's believed in physics that the "passage" of time is in our minds. But it doesn't say that all time is an illusion. But people got wind of this concept and of course they completely messes up what the concept was actually saying.
It was actually Einstein. And the passage of time, not time itself.

Relativistic effects happen to space (length contraction) and time equally. They are 2 sides to the same coin.

the effect of motion will be there
time is a measure
that we understand the event

not a force
not a substance

 

[ratiocinator]

the effect of motion will be there
time is a measure
that we understand the event

Time is an observer dependant direction through space-time. There is plenty of evidence of this and no evidence for your empty assertion that "time is all in your head".

 

[osgart]

Why do people talk themselves out of sensed reality altogether? I dont admire such nonsense, as if brilliance.

Granted senses can deceive, for lack of input but i totally doubt they are fabrications of the mind.

If there were no time then everything remains brand new in the now, and im forever young.

If there were no distance, then its too crowded in here.

And if space aint infinite, then magical nothing exists out beyond it.

And somehow math proves that things dont exist.

And we can all rest comfortably numb.

 

[Thief]

Time is an observer dependant direction through space-time. There is plenty of evidence of this and no evidence for your empty assertion that "time is all in your head".

observance.....by definition
is all in your head

time is a measurement
it cannot be anything else or more

 

[ratiocinator]

observance.....by definition
is all in your head

time is a measurement
it cannot be anything else or more

We use observations to deduce things about the world using science. That's how we can say that there is plenty of evidence for space-time and there being no separation of the two.

No amount of unevidenced assertions can justify your claims that, on the one hand "space is real enough", and on the other, "time is all in your head".

The evidence flatly contradicts you.