Scientific results here and now apply to there and then

[klutedavid]

Not only is it a deflection but a capitulation.
Your failure to demonstrate how 0.33333 recurring can be expressed by adding a finite number of terms proves it.

Not a capitulation at all.

You have a finite number with a recurring digit, so what?

That number, 0.33333, has a recurring digit. We do not say that 0.333333333333333333 has an infinite number of decimal places. Nor would we say that the recurring digits are approaching some undefined number such as an infinite number of places.

Recurring digits are no different to any other finite numbers and the same rules apply.

 

[46AND2]

Well, 1/3 can be as long as one is willing to change bases any time a repeater comes up. Transcendentals on the other hand ...

True.

 

[sjastro]

Not a capitulation at all.

You have a finite number with a recurring digit, so what?

That number, 0.33333, has a recurring digit. We do not say that 0.333333333333333333 has an infinite number of decimal places. Nor would we say that the recurring digits are approaching some undefined number such as an infinite number of places.

Recurring digits are no different to any other finite numbers and the same rules apply.

So how many recurring digits are there?

 

[essentialsaltes]

Always a natural number of course.

You mentioned Z. It's a well known set, well understood. What is its cardinality?

 

[durangodawood]

....There can never be an infinite set of positive integers as positive integers are finite numbers....

Yes. Each is a finite integer. But there's an infinite number of them.

 

[sjastro]

Infinity is not just a product of real number systems but applies to the complex numbers as well.
The complex number z = a + bi where a and b are real numbers and i=√-1 is imaginary.
Mod z or |z| = √(a²+b²) is the distance of the complex number from the origin O.
Complex numbers play a significant role in physics such a quantum mechanics.

Complex numbers are be mapped on a complex plane.

The complex plane can be extended by having the complex plane passing through the equator of a sphere (known as the Riemann sphere) and centred on the point O where z=0.

For each point z in the complex plane corresponds exactly one point on the surface of the sphere as shown in the diagram for points A and α respectively.
The point α is determined where the line connecting the north pole of the sphere P and A intersect the surface.

The distance of A from O is |z|.
As |z| increases, the point of intersection α gets progressively closer to P.
P can be considered to be the limit for very large |z| and is identified as the point ∞.
Where as the north pole of the sphere is the point ∞, the south pole is the point 0.

Since ∞ is an added point to the extended complex plane it can be used in arithmetical functions which are not possible in the real number system.
For example;
z + ∞ = ∞, z x ∞ = ∞, z/∞ = 0, z/0 = ∞.

 

[durangodawood]

Thats too hard^^^.

Must be false.

 

[BryanJohnMaloney]

Also, how can they be sure that space is the same between us and a distant object? It is quite vast. How can they be sure that there is not some type of phenomena, eddy etc distorting what we can record. We know a lot less than we think we do about a lot more than we know.

How can we be sure that you aren't a highly trained dog with an AI assistant?

 

[durangodawood]

How do we know everything isnt really the opposite of how it seems?

 

[FrumiousBandersnatch]

Infinity is not a numerical entity.

True.

A set of any finite numbers is never an infinite set, because the term 'infinite' is not numerically defined.

False; all integers are finite, but the set of all integers is infinite:

"the set of integers from 1 to 100 is finite, whereas the set of all integers is infinite" Britannica​

More technically:

"A set of elements

is said to be infinite if the elements of a proper subset

can be put into one-to-one correspondence with the elements of

. An infinite set whose elements can be put into a one-to-one correspondence with the set of integers is said to be countably infinite; otherwise, it is called uncountably infinite." Wolfram MathWorld​

 

[BryanJohnMaloney]

How do we know everything isnt really the opposite of how it seems?

I kind of noticed how this thread long ago turned into stoner chitchat, too.

 

[Sam91]

How can we be sure that you aren't a highly trained dog with an AI assistant?

I've seen multiple articles since I posted confirming many of my suppositions. I'm thinking I'm probably on the right track in highlighting the difference between facts and theory. Thanks.

 

[BryanJohnMaloney]

I've seen multiple articles since I posted confirming many of my suppositions. I'm thinking I'm probably on the right track in highlighting the difference between facts and theory. Thanks.

Gosh, having trouble with that? Well, you do need to get those under your belt before being a scientist.

First, there are no "facts" in science. there are only observations, hypotheses, conclusions, theories, models, and predictions. (There are also "laws", but "law" is an obsolete term that is only retained due to historical accident. You won't find any new "laws" promulgated in science, because our understanding of how the conclusions of science relate to reality is a bit better than in the 1700s and early 1800s. Nearly everything that would have been called a "law" at one time would now be published as a "model" or "prediction". "Law is just unspeakably arrogant--and most of the "laws" we have on the books actually only apply in special cases, meaning they aren't universal.)

What people with no clue about how science works like to natter on as "facts" are actually the conclusions and models.

 

[BryanJohnMaloney]

True.
"A set of elements

is said to be infinite if the elements of a proper subset

can be put into one-to-one correspondence with the elements of

. An infinite set whose elements can be put into a one-to-one correspondence with the set of integers is said to be countably infinite; otherwise, it is called uncountably infinite." Wolfram MathWorld

Technically, that's not a numeric definition. That's a set theory definition.

 

[Sam91]

Gosh, having trouble with that? Well, you do need to get those under your belt before being a scientist.

First, there are no "facts" in science. there are only observations, hypotheses, conclusions, theories, models, and predictions. (There are also "laws", but "law" is an obsolete term that is only retained due to historical accident. You won't find any new "laws" promulgated in science, because our understanding of how the conclusions of science relate to reality is a bit better than in the 1700s and early 1800s. Nearly everything that would have been called a "law" at one time would now be published as a "model" or "prediction". "Law is just unspeakably arrogant--and most of the "laws" we have on the books actually only apply in special cases, meaning they aren't universal.)

What people with no clue about how science works like to natter on as "facts" are actually the conclusions and models.

Maybe you should tell the folk on here that because that's the point I was making

 

[FrumiousBandersnatch]

Technically, that's not a numeric definition. That's a set theory definition.

It is only to make the point that the set of integers is a countably infinite set because its elements are in a one-to-one correspondence with the set of integers...

 

[sjastro]

Maybe you should tell the folk on here that because that's the point I was making

Really?; sounds like as bit of projection going on here.

Until recent times there was serious consideration the fine structure constant α not only varied in the past but in different regions of the universe at the same cosmological time.

α = (1/4πε₀)e²/hc;
is the strength of the electromagnetic interaction.
If α did vary was it e the electric charge, h the Planck constant or c the speed of light that varied; or all three?

By 2017 the answer based on a quasar observation was that α did not vary in the past, hence e, h and c did not vary in the past.
This is how science is done.
As to the question whether there is a spatial variation at the same cosmological time the question is still open as no other quasar candidates have been found so far.

 

[46AND2]

What I find amusing is creationists simultaneously claim that the universe is so finely tuned, it must have been designed for us, AND hang their hat on the idea that we can't know how old the earth/universe is because constants might have been different in the past.

So which is it? Finely tuned constants, or variable constants?

 

[Sam91]

What I find amusing is creationists simultaneously claim that the universe is so finely tuned, it must have been designed for us, AND hang their hat on the idea that we can't know how old the earth/universe is because constants might have been different in the past.

So which is it? Finely tuned constants, or variable constants?

https://phys.org/news/2019-11-yields-smaller-proton-radius.html

Neither. You haven't worked out measurements yet, neither macro nor micro. There can not be certainty about constants. Scientists have to work with assumptions as it can not be proven. It amazes me how scientists can have so much faith in what they can't prove, yet some atheist scientists (yes, some are Christians) scoff at the idea that other types of faith.

 

[46AND2]

https://phys.org/news/2019-11-yields-smaller-proton-radius.html

Neither. You haven't worked out measurements yet, neither macro nor micro. There can not be certainty about constants. Scientists have to work with assumptions as it can not be proven. It amazes me how scientists can have so much faith in what they can't prove, yet some atheist scientists (yes, some are Christians) scoff at the idea that other types of faith.

Minute changes in the accuracy of measurements does not help YEC. Do we know the EXACT measurements for all constants? No. Does that mean errors of orders of magnitude are still on the table? NO. As technology improves, so does accuracy. So what? The vast majority of the time, the measurements which have been improved fall within the previous error tolerances.

In order for YEC to be true, constants need to have changed by orders of magnitude, sometimes MANY orders. And we KNOW, beyond any reasonable doubt, that they have not. Because multiple INDEPENDENT lines of measurement, with vastly different mechanisms, would have all had to be different in JUST such a way, that they all come to the same wrong answer.

And you post, what? A 6%-ish difference for the size of protons? Do you have any idea how hard it is to measure a FEMTOMETER? MUCH MUCH harder than it is to measure the constants that creationists need to be ridiculously different, and are holding out hope for. It's like hoping to win a lottery that stopped drawing numbers decades ago. And the ironic thing is, nobody should want to win that lottery, cause it would vaporize the earth.