Scientific results here and now apply to there and then

[essentialsaltes]

How about you describe what infinite means.

Sure, it means "not finite".

a finite set is a set that has a finite number of elements.
{2, 4, 6, 8, 10}
is a finite set with five elements. The number of elements of a finite set is a natural number (a non-negative integer) and is called the cardinality of the set. A set that is not finite is called infinite. For example, the set of all positive integers is infinite:

{1, 2, 3, ...}

----
{1,2,3} is a finite set with 3 elements
{1,2,3,4} is a finite set with 4 elements
{1,2,3,4,5} is a finite set with 5 elements
{1,2,3,4,5,...,N} is a finite set with N elements.

As you correctly observed, "every single positive integer in that set is always followed by another positive integer."

Therefore the set of all positive integers is not finite. If it was finite, the set would end in some largest N. But we know it doesn't end. N+1 is also a positive integer that belongs in the set.

The set of positive integers does not end.
Does not finish
Is not finite
is unfinishable
is infinite
because it does not have a finite number of elements. If you think you've listed them all, you are mistaken, because (as you said) that last one "is always followed by another".

 

[essentialsaltes]

It means, God created a man not a baby. So, if you looked at Adam you would have thought, "20-30 years old" when in reality he might have been seconds old. Not deception, it is, again, simply that God didn't create a baby He created a man and with that would naturally come the appearance of age to somebody who was trying to catch God in a lie, I guess?

Don't get so defensive. I'm just trying to explore your beliefs. OK, so the reason this idea of creation 'with appearance of age' is called the Omphalos hypothesis is that 'Omphalos' is Greek for 'belly button'. Did Adam have a belly button? If he was created looking like a 25 year old, it seems unlikely that he was attached to an umbilical cord. Actually, I don't really care about belly buttons. What about scars? Did Adam have a scar on his knee from when he scraped it when he was 6 years old? Since he was never 6 years old, it seems unlikely. Was Adam created with or without scars of 'previous' injuries?

but in reality he was seconds old. Same with the mountains.

The mountains are born with scars. If they were created 6000 years ago, they bear the scars of volcanoes that never erupted. The chain of the Hawaiian Islands continues for thousands of miles (most of them being sea mounts that don't rise above the water). They were created by a 'hotspot' bubbling up lava as the ocean floor moved above it. A moving scar (if you will) of volcanic activity stretching for thousands of miles. The only active volcanoes in Hawaii are on the big island at the end of the scar. The other islands are volcanically dormant, and have been for millions of years in some cases. And the seamounts 3000 miles away have been dormant for many millions of years.

Same with the stars.

Some stars were born with scars. Or rather, we see stars that exploded long ago. If they are only 6000 years old, then they were created already dead. They were never stars.

The dinosaurs (only land dwelling) could have been brought aboard and the environment after the flood might not have been as conducive for their existence

If dinosaurs and trilobites and other long-extinct species all lived within the past 6000 years, we would expect to find human fossils along with their fossils. We do not. Why is that? We find dinosaurs with other dinosaurs. And we find humans with wolves and mammoths. But we don't find dinosaurs with modern-ish mammals.

 

[Ken Rank]

Don't get so defensive. I'm just trying to explore your beliefs. OK, so the reason this idea of creation 'with appearance of age' is called the Omphalos hypothesis is that 'Omphalos' is Greek for 'belly button'. Did Adam have a belly button? If he was created looking like a 25 year old, it seems unlikely that he was attached to an umbilical cord. Actually, I don't really care about belly buttons. What about scars? Did Adam have a scar on his knee from when he scraped it when he was 6 years old? Since he was never 6 years old, it seems unlikely. Was Adam created with or without scars of 'previous' injuries?

I wasn't trying to be defensive, just answering your questions. No, I can't imagine he had an umbilical cord, it would make no sense. He was created as a man, not as a baby or child. And no on the scars... God didn't create him with the appearance of age to fool anyone, God simply made an adult who was brand new but looking 25 years old. So no childhood scars because he had no childhood, he was always an adult.

The mountains are born with scars. If they were created 6000 years ago, they bear the scars of volcanoes that never erupted. The chain of the Hawaiian Islands continues for thousands of miles (most of them being sea mounts that don't rise above the water). They were created by a 'hotspot' bubbling up lava as the ocean floor moved above it. A moving scar (if you will) of volcanic activity stretching for thousands of miles. The only active volcanoes in Hawaii are on the big island at the end of the scar. The other islands are volcanically dormant, and have been for millions of years in some cases. And the seamounts 3000 miles away have been dormant for many millions of years.

I don't think so. We saw what Mt. St. Helens did in such a short time. From creating a "scar" to petrifying logs to creating small oil deposits.... things happened over those first 20 years that we previously were convinced took much longer. As for "dormant" volcanoes... perhaps, or perhaps the evidence has washed away. Noach's flood was world wide. Even in KENtucky, the state fossil is a Brachiopod... essentially a sea scallop. According to the timeline, if time (the actually counting where people get 6000 years from) began when Adam sinned and the clock began to tick toward what would be a 930 year life before his demise, then Noach's flood was over 1600 years after that clock begins to tick.

Listen... the author Clive Cussler (Dirk Pitt books) dug up a Civil War Ironclad one entire MILE from the Mississippi River. This boat went down IN THE Mississippi River. One mile in 130 years? That's how far the river moved? So in 1600 years? If there isn't much physical evidence one way or the other, I am not surprised at all.

Some stars were born with scars. Or rather, we see stars that exploded long ago. If they are only 6000 years old, then they were created already dead. They were never stars.

No and yes. No on the scars... yes on explosion. Adam was given dominion over all of creation. That is why Paul in Romans 8 writes that even creation itself groans as it awaits it's redemption. When Adam sinned and death was the penalty, it wasn't just Adam who would die... it was ALL he had dominion over. So all of creation began to slowly die, in scientific terms we call it the 2nd law of Thermodynamics or entropy. So plants, animals, planets, stars... all dying as a result. But all will be restored... I believe that, you don't have to.

If dinosaurs and trilobites and other long-extinct species all lived within the past 6000 years, we would expect to find human fossils along with their fossils. We do not. Why is that? We find dinosaurs with other dinosaurs. And we find humans with wolves and mammoths. But we don't find dinosaurs with modern-ish mammals.

Actually we have but the mainstream scientific world has been very quick to attempt to destroy the credibility of those who have proposed such vile thoughts... even when they had evidence.

And for the record... I am not dogmatic about the timing. While we get 6000 years from the time Adam's life had an end (after his sin) we really don't know how much time elapsed before that point. I admit, to me, it doesn't look like that much, but I could be wrong.

 

[essentialsaltes]

I don't think so. We saw what Mt. St. Helens did in such a short time. From creating a "scar" to petrifying logs to creating small oil deposits.... things happened over those first 20 years that we previously were convinced took much longer. As for "dormant" volcanoes... perhaps, or perhaps the evidence has washed away.

The problem with your hypothesis is not that something has been washed away, but that something is there. These [extinct] volcanoes and seamounts are there. Volcanos take time to build. You may know that eventually there will be a new Hawaiian island. Lōʻihi Seamount is 10,000 feet tall, but still 3,000 feet under the level of the ocean. "Lōihi began forming around 400,000 years ago and is expected to begin emerging above sea level about 10,000–100,000 years from now." And the Big Island started growing longer ago than that. And Maui started growing longer ago than that, And Oahu and all the other seamounts stretching across the ocean floor for 4,000 miles.

Actually we have but the mainstream scientific world has been very quick to attempt to destroy the credibility of those who have proposed such vile thoughts... even when they had evidence.

Can I see the evidence?

 

[klutedavid]

Sure, it means "not finite".

a finite set is a set that has a finite number of elements.
{2, 4, 6, 8, 10}
is a finite set with five elements. The number of elements of a finite set is a natural number (a non-negative integer) and is called the cardinality of the set. A set that is not finite is called infinite. For example, the set of all positive integers is infinite:

{1, 2, 3, ...}

----
{1,2,3} is a finite set with 3 elements
{1,2,3,4} is a finite set with 4 elements
{1,2,3,4,5} is a finite set with 5 elements
{1,2,3,4,5,...,N} is a finite set with N elements.

As you correctly observed, "every single positive integer in that set is always followed by another positive integer."

Therefore the set of all positive integers is not finite. If it was finite, the set would end in some largest N. But we know it doesn't end. N+1 is also a positive integer that belongs in the set.

The set of positive integers does not end.
Does not finish
Is not finite
is unfinishable
is infinite
because it does not have a finite number of elements. If you think you've listed them all, you are mistaken, because (as you said) that last one "is always followed by another".

Look at it this way.

Let the positive integers be 'n'.

So the first positive integer is n.

The second positive integer is n+1.

So we will write three terms for example.

n, n+1, n+2 a finite set

Now we will write 100 terms.

n, n+1, n+2,...,n+99 still a finite set

No matter how many terms we take into account; this positive integer set is always a finite series.

What you claim is that the positive integer set is never ending and that is impossible. A finite set of integers which is bounded by one cannot be an infinite set.

What you need to do is specify the actual term in that set that transforms a finite set into an infinite set. A set that does not end, as you say, is not really a set of course, because that is not how a set is defined.

A set is a gathering together into a whole of definite, distinct objects of our perception or of our thought—which are called elements of the set. (Georg Cantor)

Since no element of the set of positive integers can be anything other than a positive integer, the onus is on you to specify. The specific element of that positive integer set that is not a finite member.

For example, should we write the following.

{n, n+1, n+2,...,∞}

We would be incorrect as ∞ is not a positive integer. All positive integers are always finite numbers and no matter how many integers one could consider, the fact remains. That all numbers are generated by calculation and that the act of calculation is not an attribute of the infinite.

Infinite is not finite by definition and all numbers are finite numbers.

 

[klutedavid]

LOL. So that's where this is going. Only god is infinite? Should have guessed.

Your mixing the finite and infinite together, they are separated from one another by definition.

The finite is not the infinite.

No set of any objects can ever be an infinite set of objects. Simply due to the fact that any extended set of objects will never be an infinite set.

 

[Ken Rank]

The problem with your hypothesis is not that something has been washed away, but that something is there. These [extinct] volcanoes and seamounts are there. Volcanos take time to build. You may know that eventually there will be a new Hawaiian island. Lōʻihi Seamount is 10,000 feet tall, but still 3,000 feet under the level of the ocean. "Lōihi began forming around 400,000 years ago and is expected to begin emerging above sea level about 10,000–100,000 years from now." And the Big Island started growing longer ago than that. And Maui started growing longer ago than that, And Oahu and all the other seamounts stretching across the ocean floor for 4,000 miles.

Then use the same (consistent) methodology when accepting human evolution. We have apes but nothing in-between them and us... NOTHING. Supposed bones (and a very few of them at that) that are not clear cut... they are open to interpretation. And yet... you accept human evolution with no evidence at all, and then can't accept the fact that a world wide flood could have washed away evidence? The direction our technology is going Bob (I don't know your name, so I need to pick one)... if we all died today, in 100,000 years there would be very little evidence, if any, of us left. Everything that is oil based will break down. Surely some metals will be left behind that will indicate we made it to the 20th century in technology... but not much more will be left.

 

[46AND2]

Then use the same (consistent) methodology when accepting human evolution. We have apes but nothing in-between them and us... NOTHING. Supposed bones (and a very few of them at that) that are not clear cut... they are open to interpretation. And yet... you accept human evolution with no evidence at all, and then can't accept the fact that a world wide flood could have washed away evidence? The direction our technology is going Bob (I don't know your name, so I need to pick one)... if we all died today, in 100,000 years there would be very little evidence, if any, of us left. Everything that is oil based will break down. Surely some metals will be left behind that will indicate we made it to the 20th century in technology... but not much more will be left.

Even if fossilization was impossible, and we had zero bones, we would still know evolution occurred.

 

[sjastro]

Look at it this way.

Let the positive integers be 'n'.

So the first positive integer is n.

The second positive integer is n+1.

So we will write three terms for example.

n, n+1, n+2 a finite set

Now we will write 100 terms.

n, n+1, n+2,...,n+99 still a finite set

No matter how many terms we take into account; this positive integer set is always a finite series.

What you claim is that the positive integer set is never ending and that is impossible. A finite set of integers which is bounded by one cannot be an infinite set.

What you need to do is specify the actual term in that set that transforms a finite set into an infinite set. A set that does not end, as you say, is not really a set of course, because that is not how a set is defined.

A set is a gathering together into a whole of definite, distinct objects of our perception or of our thought—which are called elements of the set. (Georg Cantor)

Since no element of the set of positive integers can be anything other than a positive integer, the onus is on you to specify. The specific element of that positive integer set that is not a finite member.

For example, should we write the following.

{n, n+1, n+2,...,∞}

We would be incorrect as ∞ is not a positive integer. All positive integers are always finite numbers and no matter how many integers one could consider, the fact remains. That all numbers are generated by calculation and that the act of calculation is not an attribute of the infinite.

Infinite is not finite by definition and all numbers are finite numbers.

Argument by repetition fallacy; repeating the same mistakes doesn’t make it right.

Consider the infinite series {0.3, 0.03, 0.003, 0.0003…………} where each successive term is obtained by multiplying the previous term by 0.1.

Summing the terms in this infinite set gives;

This is an example of convergent infinite series.
Note anything unusual here?
Infinity has been assigned to a variable n, furthermore an infinite number of terms have been summed to give a finite answer 1/3 = 0.3333333…. recurring.
In order to obtain the most “accurate” answer one needs to sum over an infinite number of terms otherwise truncating the infinite series by summing over a finite range results in an answer to a number of decimal places depending on the number of terms being summed.

This is yet another example of a practical application of infinity and infinite sets which are not esoteric parameters outside mathematics.

 

[klutedavid]

Argument by repetition fallacy; repeating the same mistakes doesn’t make it right.

Finite is not infinite.

Consider the infinite series {0.3, 0.03, 0.003, 0.0003…………} where each successive term is obtained by multiplying the previous term by 0.1.

The cardinality of any set is always a natural number. There cannot exist by definition an 'infinite set'. There is no such thing as a transfinite cardinal number because infinite cardinal numbers cannot exist.

Summing the terms in this infinite set gives;

This is an example of convergent infinite series.
Note anything unusual here?

You have an upper limit of n=∞, that limit is not a finite number. So you have somehow confused the finite with the infinite. They are separate in definition and cannot be assigned together in a mathematical calculation.

Infinity has been assigned to a variable n, furthermore an infinite number of terms have been summed to give a finite answer 1/3 = 0.3333333…. recurring.

You can't assign the infinite to a variable. There is no such thing as an infinite number of terms because the infinite is not a number.

Your actually using a philosophical concept as a variable and worse as an upper limit. I repeat that infinite is not a numerical entity.

In order to obtain the most “accurate” answer one needs to sum over an infinite number of terms

There is no such thing as an infinite number of terms. How many times do I need to repeat myself. Infinite is not a number but a concept.

This is yet another example of a practical application of infinity and infinite sets which are not esoteric parameters outside mathematics.

Infinite sets do not exist either in reality or even in the imagination. An infinite set is a paradox.

 

[essentialsaltes]

n, n+1, n+2,...,n+99 still a finite set

No matter how many terms we take into account; this positive integer set is always a finite series.

Right, because there is a last element in each of your examples. But as you noted, there is always another integer.

So none of the sets you have written out is the set of all positive integers. The set we want to talk about.

The set of all positive integers is infinite, because there is no end to the positive integers. Each of them has a successor.

Since no element of the set of positive integers can be anything other than a positive integer, the onus is on you to specify. The specific element of that positive integer set that is not a finite member.

None of the set's elements is infinite. The set is infinite.

Since all finite sets have a largest element, the onus is on you to specify. What is the largest positive integer?

 

[essentialsaltes]

The cardinality of any set is always a natural number.

Excellent! What is the cardinality of the set of positive integers?

 

[klutedavid]

Right, because there is a last element in each of your examples. But as you noted, there is always another integer.

So none of the sets you have written out is the set of all positive integers. The set we want to talk about.

The set of all positive integers is infinite, because there is no end to the positive integers. Each of them has a successor.



None of the set's elements is infinite. The set is infinite.

Since all finite sets have a largest element, the onus is on you to specify. What is the largest positive integer?

There is no greatest positive integer because there is another positive integer, after every positive integer.

On and on, it goes with the set of positive integers but the set of positive integers will never attain, an infinite number of elements. Because the infinite is not a number and no count of any number can possible reach the infinite.

Finite numbers are always finite numbers and always less than the infinite, no matter how far you extend a set of finite numbers. There cannot exist an infinite set of finite numbers. That is a contradictory statement.

A horrid alloy of two very different definitions.

None of the set's elements is infinite. The set is infinite.

A mathematical paradox.

 

[sjastro]

Finite is not infinite.The cardinality of any set is always a natural number. There cannot exist by definition an 'infinite set'. There is no such thing as a transfinite cardinal number because infinite cardinal numbers cannot exist.
You have an upper limit of n=∞, that limit is not a finite number. So you have somehow confused the finite with the infinite. They are separate in definition and cannot be assigned together in a mathematical calculation.
You can't assign the infinite to a variable. There is no such thing as an infinite number of terms because the infinite is not a number.

Your actually using a philosophical concept as a variable and worse as an upper limit. I repeat that infinite is not a numerical entity.
There is no such thing as an infinite number of terms. How many times do I need to repeat myself. Infinite is not a number but a concept.Infinite sets do not exist either in reality or even in the imagination. An infinite set is a paradox.

I notice how you obfuscate posts in a flood of false definitions.
If infinite sets do not exist then show us how you can sum the finite set {0.3, 0.03, 0.003, 0.0003…………} to obtain 0.33333 recurring.

 

[essentialsaltes]

A mathematical paradox.

Nonsense.

{3, 7, 13, 29}

All of the set's elements are prime. The set is not prime. The set can have different properties from its elements.

The cardinality of any set is always a natural number.

Excellent, what is the cardinality of the set of positive integers?

 

[klutedavid]

I notice how you obfuscate posts in a flood of false definitions.
If infinite sets do not exist then show us how you can sum the finite set {0.3, 0.03, 0.003, 0.0003…………} to obtain 0.33333 recurring.

The set of any finite numbers is always a finite set by definition. I hold to the definition of 'finite' in it's strict form. A transfinite number does not exist, and there are no infinite set of numbers.

A mathematical calculation involving finite entities cannot include an infinite term.

Infinite is a non numerical term.

A set of numbers are always defined as finite numbers. The definition of 'infinite' is not the definition of 'finite', they are not the same.

All sets of positive integers are cardinal sets, and no matter how large a set one considers. That cardinal limit will always be a fixed cardinal number.

 

[klutedavid]

Nonsense.

{3, 7, 13, 29}

All of the set's elements are prime. The set is not prime. The set can have different properties from its elements.



Excellent, what is the cardinality of the set of positive integers?

Always a finite number, unless of course, you have a non finite set of numbers.

 

[sjastro]

The set of any finite numbers is always a finite set by definition. I hold to the definition of 'finite' in it's strict form. A transfinite number does not exist, and there are no infinite set of numbers.

A mathematical calculation involving finite entities cannot include an infinite term.

Infinite is a non numerical term.

A set of numbers are always defined as finite numbers. The definition of 'infinite' is not the definition of 'finite', they are not the same.

All sets of positive integers are cardinal sets, and no matter how large a set one considers. That cardinal limit will always be a fixed cardinal number.

Answer the question.
If infinite sets do not exist then show us how you can sum the finite set {0.3, 0.03, 0.003, 0.0003…………} to obtain 0.33333 recurring.

 

[essentialsaltes]

Always a finite number, unless of course, you have a non finite set of numbers.

If I define the set "Fred" to be {5, 6, 7, 8}

And I ask "What is the cardinality of the set "Fred"?" The answer is 4. It's not 4 today and 11 tomorrow. Every set has a fixed cardinality.

If I define the set "Bob" to be the set of all positive integers.

What is the cardinality of Bob?

There should be an answer that is a natural number. What is it?

 

[Sam91]

Sure, it means "not finite".

a finite set is a set that has a finite number of elements.
{2, 4, 6, 8, 10}
is a finite set with five elements. The number of elements of a finite set is a natural number (a non-negative integer) and is called the cardinality of the set. A set that is not finite is called infinite. For example, the set of all positive integers is infinite:

{1, 2, 3, ...}

----
{1,2,3} is a finite set with 3 elements
{1,2,3,4} is a finite set with 4 elements
{1,2,3,4,5} is a finite set with 5 elements
{1,2,3,4,5,...,N} is a finite set with N elements.

As you correctly observed, "every single positive integer in that set is always followed by another positive integer."

Therefore the set of all positive integers is not finite. If it was finite, the set would end in some largest N. But we know it doesn't end. N+1 is also a positive integer that belongs in the set.

The set of positive integers does not end.
Does not finish
Is not finite
is unfinishable
is infinite
because it does not have a finite number of elements. If you think you've listed them all, you are mistaken, because (as you said) that last one "is always followed by another".

From a philosophical stance one could possibly state that once you have expressed N you have bounded it, even though it does not yet have a value. You see which ever number it is, it will be only one specific integer. Thus it is finite. It will be no more, no less and will just be. N+1 will be one integer more than the value assigned to N

It shall probably only exist for a finite time... the record and memory of it shall pass away. If 'immortalised' in a very enduring substance, it will still probably not endure indefinitely. Lol

It seems quite definite to me